Imperfections in natural diamond: the key to understanding diamond genesis and the mantle

Diamond has unique physical, thermal, electrical, and optical properties with respect to other minerals and related synthetic compounds that make it extremely valuable from an economic and industrial perspective. Natural diamond that forms in the upper mantle, transition zone, and lower mantle may encapsulate mantle minerals during growth and protect them from physical breakdown and chemical alteration upon ascent of the diamond to the surface via kimberlite eruption. Such mineral inclusions serve as the only direct means to study the deep Earth and provide critical information about the pressure, temperature, and redox conditions and the chemical and isotopic composition of the mantle. Natural diamonds show a wide range of ages and thus allow one to reconstruct the history of large-scale Earth processes, such as the formation and amalgamation of Earth’s lithosphere, the onset and evolution of tectonic processes (e.g., Wilson cycles), and the recycling of C, H, and N between different primordial and crustal reservoirs. In this review, a detailed description of all types of imperfections (e.g., mineral and fluid inclusions and structural defects) and the methods by which such imperfections can be analyzed to elucidate aspects of Earth’s complex geologic history is given.


Introduction
Diamond is a naturally occurring allotrope of carbon. Several unique physical, thermal, optical, and electrical properties arise from the cubic crystal structure of diamond consisting of covalently bonded carbon (C) atoms in tetrahedral coordination. Perhaps of most notoriety is the extreme hardness of diamond making it the ideal choice for B Maxwell C. Day maxwell.day@unipd.it 1 Department of Geosciences, University of Padua, Via Giovanni Gradenigo, 6, 35131 Padua, PD, Italy cutting and polishing applications and the ultra-wide band gap of diamond, a property required for use as semi-and superconductors. Over the last several decades, diamonds have received considerable attention in many scientific fields, such as theoretical and applied physics, quantum technologies, engineering, electronics, medicine, and materials science [1]. Consequently, many advances have been made in the synthesis of diamond, particularly via chemical-vapor deposition (CVD) and high-pressure hightemperature (HPHT) methods ( [2] and references therein).
Natural diamonds form in a variety of geologic settings (Sect. 1.2); however, the majority of mined diamonds form in the deep Earth, in the lithospheric and sublithospheric mantle at depths of 120-800 km [3][4][5][6][7]. In these environments, diamonds precipitate due to reduction or oxidation or C-species (e.g., CO 2 and CH 4 ) in fluids and melts upon metasomatic (redox) reaction of such fluids with mantle rocks, such as meta-peridotites. After formation, diamonds may reside in the mantle for billions of years, during which they may undergo continued growth or dissolution depending on the type of fluids and the degree of pressure (P), temperature (T), and oxygen fugacity (f O2 ) fluctuations they are subject to. An exceedingly small proportion of diamonds are eventually transported to the surface in melts via deep-seated volcanic systems called kimberlite pipes.
Crystallographically perfect and chemically pure diamond contains minimal information about the conditions and environments in which it formed. Fortunately, most natural diamonds contain different types of imperfections that record aspects of the complex history of diamond formation, growth, residence in the mantle, and transport to the surface. Imperfections such as crystallographic point-defects associated with nitrogen (N), hydrogen (H), and boron (B) impurities provide information about the residence temperature/time of diamond. The most informative imperfections are mineral and fluid inclusions which allow direct observation of the geochemical and mineralogical properties of the otherwise inaccessible deep Earth. Other mantle derivatives such as xenoliths or xenocrysts are susceptible to alteration and mechanical breakdown during transport to the surface. In contrast, diamond is chemically inert and physically robust providing the ideal time capsule to preserve inclusions and fluids associated with diamond formation in the mantle underlying different geographic regions (diamond are observed in six continents) over a wide range of geologic time.
The hierarchical organization of this review is shown in Fig. 1 where the topic of each chapter (1)(2)(3)(4)(5) is related to the following and preceding chapter by arrows. In Chapter 1, a brief introduction of the structure and composition of the mantle gleaned from diamond research is given in addition to an overview of the geologic setting of diamond formation. In Chapter 2, the economic and scientific value of diamond is explained based on its physical, thermal, optical, and electrical properties. Moreover, the nomenclature and classification schemes used in the geological study of diamonds are given based on properties, including textures, morphology, crystallinity, N-aggregation state, host (or parental) rock types, inclusion mineralogy, and geologic settings of formation. In Chapter 3, imperfections observed in natural diamond are discussed and divided into three groups: (1) Intrinsic imperfections (e.g., edge dislocations due to plastic deformation).
(2) Extrinsic imperfections (e.g., N-, H-and B-related defects). In Chapter 4, different models for lithospheric and sub-lithospheric diamond formation at varying conditions (P, T, and f O2 ) in the mantle are discussed using data from primarily (3). In Chapter 5, the imperfections observed in natural diamond, primarily mineral and fluid inclusions and isotopic data of C and N, are related to large-scale, deep Earth processes, such as (1) ancient and modern carbon (re)cycling in the mantle and its relation to the onset and evolution of different styles of plate tectonics in the Archean and Proterozoic, (2) evolution of recycled carbon reservoirs and associated C-bearing, diamond-forming fluids sources in the mantle through geologic time, and (3) mobilization and transport of diamond and associated fluids in the mantle, and the C-speciation for different types of diamond-forming fluids and melts.
The primary focus of this review is to relate the properties of imperfections in diamond to the structural and compositional evolution of the mantle through geologic time. For the purposes of brevity, we direct our review to monocrystalline, lithospheric, and sub-lithospheric diamonds. However, experimental data from other types of diamonds (e.g., fibrous and synthetic diamonds) are invoked where useful. Although there are numerous reviews on imperfections in diamond, particularly inclusions, and their relation to mantle geodynamics, few evaluate all types of imperfections. A notable exception is the recent Review in Geochemistry and Mineralogy, ed. 88, Diamonds: Genesis, Mineralogy and Geochemistry [8], much of which is reviewed in this paper.

Structure and composition of the mantle: insights from diamond
Since the work of Richard Dixon Oldham and Andrija Mohorovičić in the early twentieth century (e.g., [9,10].), who provided evidence for the existence of a crust (with thickness of 6-70 km), mantle (down to 2900 km), and core (2900-6371 km), geophysical methods have remained the principal tool for investigating the structure of the Earth. Such methods rely on the behaviour of seismic waves as they propagate through mediums of different density but are inherently indirect as data (e.g., mineralogical composition of the mantle) can only be inferred rather than directly measured or observed. Direct methods involve the study of xenoliths or xenocrysts, rock fragments, or crystals from the upper mantle that have been transported to the surface by volcanism (kimberlites or lamproites) and/or tectonic exhumation. Xenoliths are predominately from the upper mantle and of peridotitic or eclogitic paragenesis containing mostly olivine, clinopyroxene, orthopyroxene, and garnet [11][12][13][14]. Thus far, mantle xenoliths from depths down to~300 km have been described (e.g., [15][16][17]) but not from depths representative of the lower mantle. Furthermore, chemical alteration (e.g., recrystallization and isotopic re-equilibration) of xenoliths and xenocrysts due to interaction with volatile-rich fluids or melts associated with the kimberlitic system is common [12,[18][19][20][21]. Thus, caution must be used when making geochemical, petrogenetic, or geochronological inferences about mantle xenoliths.

Geologic settings of diamond formation
On Earth, natural diamonds form in four distinct geologic settings; (1) the lithospheric mantle; (2) the sub-lithospheric mantle; (3) ultra-high-pressure metamorphic (UHPM) terranes (orogenic belts); and (4) in meteorite impact sites. The source (provenance) and speciation of C, mineralogical (e.g., graphite) or molecular (e.g., CH 4 ), and the means by which carbon is subject to pressure and temperature (P/T) conditions conducive to formation of diamond, is different for each setting. Lithospheric diamonds form in the continental lithospheric mantle and sub-lithospheric diamonds form in the sub-lithospheric mantle, most commonly in the base of the upper mantle and transition zone [6]. Diamonds are transported to the surface in magmas associated with kimberlites, and to a lesser extent lamproites and lamprophyres, which are usually much younger (on average, 45 Ma to 1.2 Ga, [26]) than lithospheric diamonds, as old as 3.5 Ga [23][24][25] and sub-lithospheric diamonds which are largely Mesoproterozoic [71]. UHPM diamonds form in much shallower environments in the lithosphere where orogenic processes produce the P/T conditions necessary to convert carbon, sourced from the crust (e.g., metasedimentary protoliths), to diamond [72]. Impact diamonds form due to a rapid increase in P and T from collisions (e.g., with meteorites, asteroids, and planetary bodies) involving carbon-bearing materials [73,74].
Most diamondiferous kimberlites occur in the central regions of seismically stable, Archean and early Proterozoic cratons. A craton as defined by [36], are regions of the continental crust underlain by 150-200 km-thick lithospheric mantle that have been tectonically stable since 1 Ga. Below the nuclei of these cratons, the lithospheric mantle protrudes into the deeper convecting mantle to depths of 250-300 km, much deeper than other regions of surrounding continental or oceanic lithosphere (~110 km under the oceanic lithosphere) [79][80][81][82]. These features, called lithospheric mantle keels (Fig. 3), formed shortly after the onset of Archean plate tectonics. During the subduction of oceanic lithosphere, a layer of relatively hot (~200°C hotter than current mantle temperatures) and buoyant [79], melt-depleted lithospheric mantle separates from the colder dense slab and is emplaced beneath the adjacent continental lithosphere where it cools to temperatures in the diamond stability field (900-1400°C at lithospheric mantle pressure, [42]) and stabilizes the overlying cratonic lithosphere [83]. Formation of Paleo-Archean mantle keels and some of the oldest known diamonds (e.g., 3.5 Ga, Ekati mine, Slave Craton) occurred before the onset of plate tectonics, and thus, the mechanisms by which they form do not involve subduction; this is discussed in more detail in Chapter 5.
Lithospheric mantle keels are located below the graphite-diamond transition depth and may induce kimberlite magmatism in the mantle at depths greater than would be possible beneath younger (and thinner) lithosphere. The mantle keel is continually supplied with C-rich melts derived from the deeper convecting mantle and from the partial melting of the subducting lithospheric slab. Consequently, mantle keels are the ideal environment for diamond formation and transport via kimberlitic eruption. Clifford [84] recognized that most diamond-bearing kimberlites occur in stable cratonic nuclei overlying sections of relatively thick, melt-depleted lithospheric mantle or what are now called mantle keels, this correlation is referred to as Clifford's Rule. Fig. 3 A cross-section of the Earth's crust down to the lower mantle. Continental and oceanic crust is shown in beige and gray, respectively, and the upper mantle is separated into two mineralogical facies, spinel (purple) and garnet (pink), and the asthenosphere, transition zone, and lower mantle are shown in red, orange, and yellow, respectively. Small volume melts and upwelling magmatic systems are shown with dark red circles and larger U-shaped symbols. The area underlain by the cratonic mantle keel is shaded in gray; here, the cool cratonic lithosphere may extend to depths greater than 200 km and act to decrease the pressure (and depth) and which graphite transforms to diamond (white dashed line); this region is commonly referred to as the diamond window. Diamond (or diamond-forming fluids) may also form from partial melting and dehydration of subducted oceanic crust. Three major phase transitions are shown at3 00 km in the upper mantle, at~410 km at the upper mantle-transition zone boundary and at~660 km at the transition-zone-lower mantle boundary with black arrows. Modified from Stachel and Harris, [42] Lithospheric diamonds form in mantle keel environments at depths of 120-200 km (average depth of 175 ± 15 km) and at an average temperature of 1160 ± 100°C and pressure of 5-6 GPa [5,43,85]. Sub-lithospheric diamonds or super-deep diamonds (SDDs) form below the sub-continental lithospheric mantle (SCLM) in the convecting mantle at depths of~300-800 km and at average temperatures and pressures of 1200-1500°C and 9-11 GPa [6,7,86,87]. However, the majority of SDDs form around the transition zone at 410-660 km [88].

Diamond: properties, description, and classification
Over the last 15 years,~7400 articles about diamond were published in geology, mineralogy, geochemistry, geophysics, and mining-related journals, accumulating an average of~500 citations per year. The diamond geology literature has a relatively high data-density and consequently, a complex and multi-faceted nomenclature has emerged. An understanding of how different types of diamonds are described and classified is crucial before one attempts to familiarize themselves with the most recent scientific works on the processes and environments related to diamond genesis.

What is diamond and why is it valuable?
In diamond, each C atom forms four covalent bonds with neighboring C atoms to form C-tetrahedra. Tetrahedra link to form a relatively small unit cell that contains eight carbon atoms in cubic symmetry (space-group Fd 3 m) in which all angles of the cell are 90°and all sides have a length of 3.567 Å [89]. The crystal structure of diamond can be simply described as two interpenetrating face-centered cubic lattices displaced with respect to one another along the body-diagonal of the cell by 1/4 the length of the diagonal. This displacement length is equal to the C-C bond length which is~1.54 Å (Fig. 4) [89].
The behavior of carbon in the form of graphite, diamond, liquid, and vapor as a function pressure and temperature is well understood (Fig. 5). The structural description of diamond given above is based on observations made at room temperature. However, when subject to extremely high temperatures and/or pressures (P/T conditions in the diamond stability field, Fig. 5), the unit-cell parameters of diamond may vary as C-C bond lengths and angles change to equilibrate with the increased P/T conditions. Diamonds form in the deep mantle at extremely high pressures and temperatures and thus, are thermodynamically stable at such conditions compared to those at the surface (surface temperature and pressure (STP) = 20°C and 0.10 MPa).
The thermodynamically stable allotrope of carbon at surface conditions is graphite and the famous slogan diamonds are forever, is not entirely true as diamonds are considered metastable at surface conditions. Although the rate at which diamond transforms to graphite at surface P/T conditions is almost zero, given enough time (on scales of billions of years), diamond will inevitably breakdown due to stochastic Fig. 4 Crystal structure of diamond in which all C atoms are in tetrahedral coordination and linked to one another by C-C bonds with lengths of 1.54 Å. Dashed red lines outline a single unit cell with edge lengths of 3.567. Structure generated from ATOMS V6.4 with data from Straumanis and Aka [89] Fig. 5 Theoretical phase diagram of C as a function of pressure (GPa) and temperature (1000 K). Modified from Zazula [460] processes. The diamond-to-graphite phase transition has a Gibb's free energy ( G°= − 2.9 kJ mol −1 ) [90] close to zero, as the thermodynamic stabilities of diamond and graphite at surface P/T conditions are similar; nevertheless, the reaction is exergonic and thus spontaneous. However, for this transformation to occur, a relatively large energy barrier (~370 kJ mol −1 ) [90], related to the breaking of C-C bonds, must be overcome. Diamond in the presence of O 2 atmosphere may decompose to produce CO 2 ; this reaction is also spontaneous but more thermodynamically favored as G°= − 397 kJ mol −1 [90]. This was first shown by Antoine Lavoisier in 1772 who proved that diamonds were composed principally of carbon by showing that the same amount of CO 2 (per gram of material) is produced by burning diamond and graphite. It follows that, at surface P/T conditions, diamond is kinetically stable but thermodynamically unstable.
The diamond-to-graphite energy barrier is easily overcome by increasing temperature. However, the fast ascent (eruption) rates of kimberlitic systems, delivering diamonds from variable depths to the surface, prevent transformation of diamond to graphite until it reaches lower temperature environments near the surface. A significant increase in pressure is required to convert the diamond-to-graphite transformation from an exergonic-to-endergonic (non-spontaneous) reaction and eventually to convert metastable graphite to diamond (Fig. 5). Several studies suggest diamond may undergo additional phase transitions to body-centered cubic structures at extreme pressures (~1100 GPa) or melt to form a metallic fluid (liquid C) at extreme temperatures and pressures (~50,000 K and~1000 GPa) [91]. However, natural diamonds form at pressures that do not exceed~23 GPa [92], respectively, and thus, such phases are not considered here. Lonsdaleite, what is generally considered the hexagonal polymorph of diamond, is typically observed as inclusions in diamonds associated with meteorite impacts. However, recent work [93,94] suggests that lonsdaleite is not a polymorph of diamond but instead a mixture of micro-to nano-scale cubic and hexagonal diamond layer stacking and graphitic domains.
Why are we interested in diamond? In general, people are interested in natural and synthetic diamond from (1) a scientific perspective and (2) an economic perspective. In this review, we will focus almost entirely on (1), but a brief description of how the utility and aesthetics of diamonds contribute to their value is warranted. The economic value of diamond is a function of its unique physical, optical, thermal, and electrical properties, each of which useful for particular applications. Here, a description of how these properties arise from aspects of the chemical and crystal structure of diamond is given.

Physical properties
It is generally accepted that diamond is the hardest mineral, and thus the most durable naturally occurring material. The extreme hardness of diamond makes it the ideal choice for abrasives (e.g., grinding, polishing, and drilling applications), cutting tools, and coatings to prevent mechanical wear or corrosion of computer (e.g., hard disks), mechanical (e.g., ball-bearings), or jewellery-related components. The extreme strength of diamond has even inspired several truss designs based on its cubic crystal structure.
The hardness of diamond is best explained in terms of elasticity, which describes how a mineral deforms reversibly (strains) in response to an applied pressure (stress). Stress and strain are linearly related during elastic deformation and non-linearly related during plastic (non-reversible) or brittle deformation, both of which may occur in diamond. The elasticity of minerals is related to the bulk modulus, K 0T (GPa), a measure of volume change in response to a compressive force. At room temperature, diamond has an extremely high bulk modulus, and harder and more rigid materials have a higher K 0T as they show a smaller volume change during compression. For diamond, K 0T = 444.0 (± 2) GPa [95], significantly larger than common rock-forming minerals, such as quartz (K 0T = 37.0 (± 0.3) GPa, [96]), olivine (K 0T = 124.7 (± 0.9) GPa, [97]), and plagioclase feldspars along the anorthite-albite join (K 0T =5 2-82 GPa, [98]).
Although the superior hardness and incompressibility of diamond is often solely attributed to strong C-C bonds, it is actually the geometry of C-C bonds in the diamond lattice that results in such desirable properties. In diamond, all four valence electrons are involved in bonding via sp 3 orbital hybridization. In graphite each C atom is bonded to three other C atoms via sp 2 -bonds to form graphene-type sheets. As only three valence electrons are involved in C-C bonding, the fourth becomes delocalized across the entirety of the sheet. Delocalized electrons contribute to bonding within the sheet and result in C-C bonds that are stronger than those in diamond. So why is diamond so hard (Moh's = 10) and graphite so soft (Moh's = 1-2)? In graphite, movement of delocalized electrons results in adjacent sheets with opposite dipoles and the consequent bonding of such sheets via Van der Waals dispersion forces. This type of bonding is relatively weak and predisposes graphite to breaking (cleaving) along planes parallel to each sheet. In diamond, all bonds are covalent and arranged, such that there are no orientations in diamond more or less susceptible to compression in response to an applied stress. Diamond contains the greatest number of atoms per unit-volume with an atomic density of 1.7 × 10 23 atoms/cm 3 [90]. However, the atomic packing fraction, a comparison between the volume of the unit cell and the sum volume of each atom in the unit cell, is low (34%) [90] compared to closepacked structures (74%) and the density of diamond (3.5 g/cm 3 ) is also relatively low, surpassed by common constituents of the crust, such as fayalite (4.39 g/cm 3 ), ferrosilite (3.95 g/cm 3 ), magnetite (5.15 g/cm 3 ), pyrite (5.01 g/cm 3 ), and spessartine (4.18 g/cm 3 ) [99].

Optical properties
Over the last 30 years, advances in the production of synthetic diamonds, specifically by chemical-vapor deposition (CVD diamonds), have allowed for the efficient production of high-quality diamond, free from the optical and structural defects that are often observed in other types of synthetic [e.g., high-pressure-high-temperature (HPHT) diamonds] or natural diamond [2]. Consequently, the optical applications of diamond have expanded and are used in X-ray windows, optical lenses, antireflection coatings, and attenuated total reflection (ATR) spectroscopic applications.
The aesthetic value of diamond is due to its optical properties, specifically those related to color and lustre. Natural diamonds can occur in many colors including, red, pink, purple, yellow, brown, blue, white, black, and, of course, colorless. Pure, perfect diamond is transparent from the UV (225 nm) to the far infrared spectrum and is thus colorless [100]. Chemical impurities (e.g., substitutional N, see Sect. 2.2.4), mineral inclusions, and structural defects (e.g., color centers) scatter visible light and impart color in diamond, some more desirable and rare than others. Type I diamonds contain N impurities which aggregate with site vacancies to different degrees and typically result in a yellow to brown or colorless diamond [101]. Type II diamonds contain no measurable amounts of N and may show pink, red or brown coloration due to structural defects (e.g., lattice dislocations). Type II diamonds may also contain B impurities which results in a light blue diamond, although extremely rare. Microinclusions of graphite and sulphides may result in dark-brown or black diamonds and fractures, and structural defects and micro-fluid inclusions may result in a cloudy or white appearance [101]. Diamond has a high refractive index (~2.418 at room temperature) and dispersion factor (0.044) in the visible spectrum [100]. These properties, in combination with reflection due to faceting, results in the adamantine luster of diamond and prismatic appearance that many gemologists refer to as the diamond's fire. Numerous treatments, including radiation exposure, HPHT and LPHT annealing, and surface coatings, are used to enhance the color of natural and synthetic diamonds, and a detailed review of these procedures is given by [102,103] and [101].
Pristine, defect-free diamonds (and other materials with the diamond structure) have no dipole moment and thus no infrared active phonons that correspond to a fundamental lattice vibration (one-phonon absorption) [100,101]. However, infrared light may excite two or more higher order lattice vibrations (anharmonic multiples of the fundamental lattice vibration) to produce IR-active two-and three-phonon absorption regions (~1500-4000 cm −1 ) that are observed in the FTIR spectra of diamond. As is shown in Fig. 6, the intensity of each multiphonon absorption signal decreases with frequency. The introduction of lattice impurities, such as N, B, and H, results in absorption due to N(B)-C stretching and bending vibrational modes in the one-phonon region  (3 700 to 2650 cm −1 ) and two-phonon region (~2650 to 1600 cm −1 ) due to intrinsic lattice vibrations. The spectrum of the Type I diamond also shows absorption in the one-phonon region (~1400 to 1000 cm −1 ) due to N defects ( Fig. 6) from~1000 to 1400 cm −1 or at higher frequencies (e.g., 3107 cm −1 ) for Hrelated stretching modes [101]. Analysis of IR signals in the one-phonon region is the principal means by which diamonds are classified by type (e.g., [104]) (Sect. 2.2.4).

Thermal and electrical properties
Natural diamond has an extremely high thermal conductivity of~2000 W (mK) [105] due to the combination of strong covalent C-C bonds and a relatively low density compared to related cubic structures. This thermal conductivity is four-to-five times larger than the commonly used metal conductors, such as copper, silver, and gold. Diamond also has a very low coefficient of thermal expansion [reported as α (K −1 )], that is the degree of volume change due to increasing temperature. For diamond, α = 0.267 × 10 -5 K −1 , which is significantly lower than any other mineral, for example, rock-forming silicates where α =~3 × 10 -5 K −1 [95,96,98]. These properties have made diamond an attractive solution for heat-sink applications in electrical devices (e.g., high-voltage circuitry, laser diodes, transistors, and supercapacitors).
Diamond also has unique electrical properties most of which are related to its ultrawide band gap (5.47 eV) between the valence and conduction bands [101] (Fig. 7). For non-metals, movement of electrons across the band gap into the conduction band is required to allow electrons to move freely throughout the crystal and act as charge carries to increase the electrical conductivity of the material. In electrical conductors, bands overlap, and electrical conductivity is high. In diamond, a relatively large excitation energy, 5.47 eV (i.e., temperatures in excess of 1000°C or UV light where λ < 0.23 μm) [100] is required to allow electron transfer between bands, and thus, most diamonds are considered insulators. However, at lattice defects associated with specific impurities, specifically B and N, electron charge-transfer processes increase the overall electrical conductivity of the diamond, such that it acts as a semiconductor Fig. 7 The energy-level schematic of perfect (defect-free) diamond where the valence band is filled, and no electrons occupy the conduction band. Incident UV light (hv) with an energy ≥ 5.47 eV can excite electrons (e − ) from the valence band to the conduction band leaving behind a positively charged hole (h + ) in the valence band. To provide an example of donor-acceptor (charge-transfer) processes, a substitutional N atom with a neutral charge, N 0 s is shown and may donate an electron (1.7-2.2 eV) to the conduction band to produce a positively charged, N + s defect. A substitutional B atom with a neutral charge state, B 0 s is shown and may accept an electron (0.39 eV) from the valence band to produce a positively charged hole (h + ) and a negatively charged, B − s defect as opposed to an insulator. In fact, as little as 1 ppm B is required to produce diamond semiconductors and HPHT polycrystalline diamond superconductors have been synthesized using different B-doping methods [106]. The electrical behavior of impurities also influences the color of diamond. For example, impurities such as N contain extra electrons with respect to C, and these electrons are not directly involved in N-C bonding (i.e., lone-pair electrons) and are donated to the conduction band with relatively smaller excitation energies (N donor = 1.7-2.2 eV) [101] (Fig. 7). Other atoms such as B may accept electrons from the conduction band (B acceptor = 0.39 eV) [101] (Fig. 7), and these donor-acceptor (charge-transfer) processes require absorbance of visible light and thus change the color of diamond.

Diamond description, nomenclature, and classification
There are several schemes used to describe and classify diamonds, each focusing on different properties of diamonds, e.g., textures, morphology, crystallinity, N-aggregation state, or geological features such as host (or parental) rock types, inclusion mineralogy, and geologic setting of formation. Each of these schemes has different applications for each sub-discipline of geological research. For example, if one is studying diamond dissolution features, classifying and describing diamonds based on secondary growth morphologies and/or surface textures may be more useful and informative than classification based on the N-aggregation state. It is commonplace in geology to broadly classify diamonds as lithospheric or sub-lithospheric based on the depth at which they formed as this provides information about the geochemistry, mineralogy, and P/T conditions of the upper mantle (lithospheric diamonds) or transition zone and lower mantle (sub-lithospheric diamonds).
The earliest detailed recording of diamond classification dates to third century BC India, where the value of diamond was determined by its color and assigned a name corresponding to a social class; for example, colorless diamond was considered most valuable and associated with aristocracy. Since the early 1900s, experimental work has been conducted relating the color, lustre, and luminescence of diamond to the absorption of visible, UV, and infrared light. In the 1950s, the Gemological Institute of America developed a classification scheme to grade the quality of diamond based on The Four C's; color, clarity, cut, and carat (mass). In the following sections, classification schemes based on different criteria commonly used in the geological research of diamond will be described.

Primary morphologies and surface features of monocrystalline diamond
The journey of natural diamond from the deep Earth, where nucleation and primary growth occurs, to the surface via kimberlitic eruption is chemically and physically complex. Fortunately, natural diamonds have an exceptionally wide variety of morphologies and external (surface) and internal features which provide information about the types of fluids/melts and mechanisms related to diamond formation and growth and those that may cause physical or chemical breakdown (e.g., dissolution) of the diamond during transport to the surface. Such features can be broadly classified as primary or secondary and, in this section, and the following, a description of the common primary and secondary growth morphologies and textures observed in natural diamonds is given.
Primary morphologies represent the initial growth phase(s) of diamond which is controlled by the cubic symmetry of the diamond crystal structure (Sect. 2.1). As first postulated by Haüy and Bravais in the mid-nineteenth century, crystal faces tend to be parallel with planes that have a relatively high density of lattice points (or crystallographic sites) [107]. These faces grow relatively slowly and are expressed in the morphology of the crystal as the faster growing faces grow-out of the crystal [108]. This is the case for the (111) octahedral face of diamond which grows relatively slowly, consequently, most monocrystalline diamonds have an octahedral habit [108] (Fig. 8a). However, the growth rate of diamond faces is also influenced by the P/T conditions, fluid composition, speciation (and availability) of C in the growth medium, and crystallographic defects, and numerous monocrystalline diamond morphologies are observed [109]. Cubic diamonds are less common than octahedral diamonds and are typically referred to as cuboid as they are often poorly developed with rounded edges and irregular, straited faces [110]. Where both growth forms are operative during growth, cubo-octahedral diamonds may form (Fig. 8b), in some cases, such morphologies are not immediately recognized by external examination but are easily revealed by analysis of internal growth structure via cathodoluminescence (CL). If intergrown Fig. 8 A a two well-formed, equant octahedral diamonds, b cubo-octahedral or cuboid diamond, c set of macles showing rounded edges suggestive of dissolution and/or resorption (tweezer tip for scale), and d cathodoluminescence (CL) image of complex, non-concentric growth zonation patterns suggesting a complex growth history that likely involved several discrete crystals (for each growth center) before they became intergrown to form this octahedral diamond. Modified from Harris et al. [108], image a from Thomas Hunn Co., b from Dmitry Zedgenizov (Sobolev Institute of Geology and Mineralogy), c from Anetta Banas (University of Alberta), and d from Zhang [461] monocrystalline diamond crystals are aligned along crystallographic directions, they are referred to as twinned diamonds, and if they are not aligned, they are referred to as diamond aggregates [108]. Contact twinning, described by the spinal-twin law, is most common and referred to as macles when observed in diamond (Fig. 8c). Macles form from faceted growth on the [111] face, and in some cases, multiple macles may become intergrown to form unique diamond morphologies (e.g., Star of David diamonds) [108]. Monocrystalline diamonds that do not exhibit an external crystallographic habit are termed irregular diamonds [108] (not to be confused with irregular diamonds described in Sect. 3.2). Such irregularity is due to dissolution or fracturing, or in some cases a combination of both and is related to physical damage during eruption or dissolution [111].
Octahedral diamonds exhibit three main types of surface features; triangular plates, imbricated surfaces, and pyramids [108]. Triangular plates grow on the octahedral faces of diamond and the size of each triangle decreases in the direction of growth [112]. Imbricated surfaces are produced when the growth of triangular plates is disrupted, and pyramids are formed where triangular plates do not cover the entirety of the basal octahedral face [108]. As well-formed cubic and cubo-octahedral diamonds are relatively rare, attributing their surface features to primary or secondary growth features is difficult and will not be discussed here.
Investigations of the internal features in diamond via analytical methods such as cathodoluminescence and X-ray tomography are particularly useful for understanding the role of impurities such as N on the episodic growth and deformation of diamond. Diamonds often show concentric and/or non-concentric (polyconcentric) growth zonation (Fig. 8d), where each zone may show significant compositional differences (N and B content) and ages (> billions of years). Diamonds also often show deformation features, such as lattice dislocations, stacking faults, and plastic deformation features) which provide information about mantle annealing times and temperatures (e.g., [53,113]). Specific features associated with plastic deformation will be discussed in Sect. 3.2, and readers are referred to [108] for a complete review of primary morphologies and related features.

Secondary morphologies and surface features of monocrystalline diamond
Secondary morphologies of monocrystalline diamond are formed primarily by dissolution in a corrosive fluid or kimberlitic melt. Moore and Lang [114] were the first to show that dodecahedral diamonds are produced by dissolution of octahedral diamonds. Dissolution of octahedral diamonds involves reduction of each octahedral face to a vertex, which appears as a triple point between three rounded rhombic faces. A linear feature, called the medial line, occurs across the diagonal of each rhombic face [108]. If one assumes the medial line represents the intersection of two crystal faces, the secondary growth morphology has 24 faces and is best described as a tetrahexadron (THH) [115] (Fig. 9a). If the medial line is not considered representative of the intersection of two crystal faces, the diamond has 12 faces and is best described as a dodecahedron [115] (Fig. 9b). Regardless of how one describes the secondary growth morphology, in almost all cases, increasing degrees of dissolution result in more rounded diamonds.
Surficial dissolution features on octahedral diamonds include shield-shaped and serrate laminae, trigons, and hexagons [108]. Shield-shaped and serrate laminae are produced from dissolution of triangular plates and imbricated surfaces, respectively. Trigons are arguably the most commonly observed and best understood dissolution feature in octahedral diamonds. Trigons are produced by crystallographically controlled dissolution etching and their orientation is a function of temperature and f O2 [116]. Positive trigons (Fig. 9c) are triangular pits with the same orientation as the octahedral face on which they occur, and negative trigons (Fig. 9d) are rotated 180°w ith respect to the octahedral face [117]. X-ray topography experiments suggest that trigons form on areas of the octahedral face predisposed to etching due to the presence of structural dislocations or plastic deformation lines [118][119][120]. The dissolution conditions responsible for the formation of positive and negative trigons are likely different; at boundary conditions, a positive and negative contribution to trigon formation results in hexagons, six-sided pits that develop on the octahedral faces [121]. Cuboid diamonds contain tetragons rather than trigons and are similarly divided into positive Fig. 9 A a back-scattered electron (BSE) image of a tetrahexahedroid (THH) diamond, b vertex of a dodecahedroid diamond, adjoined by three rhombi produced by dissolution of an octahedral face to produce dodecahedroids and eventually rounded THH morphologies with progressive dissolution, c BSE images of an octahedral diamond with positive trigons, and d octahedral diamond with negative trigons. a, b, and d modified from Harris et al. [108], image (a) from Yana Fedortchouk, b from Karen Smit, and d from Evan Smith (GIA). c modified from Khokhryakov and Palyanov [462] and negative tetragons based on their orientation about the cube edge [122]. In general, dissolution of diamonds to form dodecahedral or THH morphologies is accompanied by the formation of additional surface dissolution features, such as terraces, hillocks, plastic deformation lines and planes, corrosion sculptures, shallow depressions, ruts, micro-disks, and frostings. A review of these features is given by [108].

Polycrystalline diamond aggregates and fibrous diamonds
In this paper, we review work on primarily monocrystalline diamond for the purposes of brevity. However, polycrystalline diamond aggregates (PDAs) and fibrous diamonds and their mineral and fluid inclusions contain a wealth of information regarding the composition of fluids associated with diamond formation. Consequently, they are described here briefly and invoked in later discussion when useful.  [52] and c modified from Mikhail et al. [127] Fibrous diamonds consist of parallel fibers that may or may not comprise the entirety of the diamond (fully fibrous, Fig. 10a) or grow over non-fibrous monocrystalline diamonds to produce coated diamonds (Fig. 10b). Fully fibrous diamonds are cuboid and consist of fibers closely aligned to the diamond axis [123]. Coated diamonds commonly consist of an inner monocrystalline octahedral core and a fibrous overgrowth in which fibers are oriented perpendicular to the octahedral faces [52,123]. In some cases, octahedral monocrystalline growth may occur over a fibrous cuboid core. Although poorly understood, the boundary between monocrystalline and fibrous growth in coated diamond likely represents major changes in the growth conditions. Fortunately, fibrous diamond is particularly well suited for incorporation and preservation of fluid and melt microinclusions which are central to recent works aimed at understanding the composition and redox state of fluids related to diamond formation (see [52] and references therein).
Polycrystalline diamond aggregates (PDAs) are rocks (mantle xenoliths) in which the dominant mineral is diamond (Fig. 10c) [124]. Following classical petrographic nomenclature, they are best described as diamondite [125]. However, akin to much of the geologic nomenclature, it is still commonplace to use rock names that originate from industry. For example, PDAs may be classified as boart if they are not gem quality but still economically viable for use in cutting or abrasive tools. Boart may be classified as stewartite or framesite based on the presence or absence of magnetic minerals, respectively [124]. Carbonados comprise another groups of PDAs and are typically black in color, contain a strange suite of minerals inclusions with crustal and metasedimentary provenance, and occur in Mid-proterozoic metaconglomerates from only a handful of localities [124]. PDAs form by rapid nucleation and growth from C supersaturated fluids [126] resulting in syngenetic intergrowths of diamonds with other minerals, a feature not typical of monocrystalline diamond. In general, PDAs are δ 13 Cdepleted, δ 15 N-enriched, have high N concentrations, and have variable N-aggregation states compared to monocrystalline diamonds [127]. Whereas slow-growing, zoned, monocrystalline diamonds provide information about the evolution of the diamond-forming environment through time, PDAs provide similar information corresponding to short moments in time when PDAs formed and/or grew. Fig. 11 Structural configuration of a C-centers which consist of single, N s atoms that form three identical N-C bonds and a fourth, significantly longer, N-C bond shown with the dashed black line, b A-centers which consist of two adjacent N s atoms which are not bonded to one another as shown with the red dashed line, c B-centers which consist of four N s atoms around a C-vacancy; here, dashed black lines do not indicate bonds and simply serve as a visual guide, and d singular B s atoms that form three identical B-C bonds and one slightly shorter (98% shorter than a C-C bond) B-C bond. Structures generated from ATOMS V6.4 with data from Straumanis and Aka [89] (e.g., [131,132]). In Sect. 3.1.1, a detailed discussion of the some of the less common defects, including those that belong to the VN x H y family will be discussed.

Classification of lithospheric and sub-lithospheric diamond based on inclusion paragenesis
As discussed in Sect. 1.2, it is commonplace to classify natural diamond as lithospheric or sub-lithospheric based on the geologic setting in which they form. Lithospheric diamonds typically show well-formed octahedral and cubo-octahedral morphologies. Sub-lithospheric (super-deep) diamonds are poorly formed, irregularly shaped, and often have several growth centers with non-concentric zonation due to repeated cycles of dissolution and re-growth in the convecting mantle [6,108]. The irregular morphology of SDDs may also be due to fracturing during brecciation at shallow (lower temperature) environments in the kimberlite system [111]; despite the plasticity of diamond at temperatures > 900°C, Shirey [133] has shown that deep-seated earthquakes may also result in brittle fracturing of SDDs in the mantle.
One may further classify lithospheric diamond based on the associated mineral assemblage. Lithospheric diamonds have one, or a mix, of the following parageneses; peridotitic, eclogitic, and to a much lesser extent, websteritic. Following Stachel [134], these parageneses are characterized by the following mineral assemblages: Peridotitic: Cr-pyrope, forsterite, enstatite, Cr-diopside, Mg-chromite, and Fe-Ni sulphides. These diamonds can be further subdivided as harzburgites, lherzolites, and wehrlites based on the occurrence of clinopyroxene and the major-element composition (Cr and Ca) of garnet [135][136][137]. However, the presence of particular inclusions, such as Fe-Ni sulphides, cannot be used to determine paragenesis in the absence of other inclusion minerals.
Websteritic: almandine-pyrope, diopside-augite, enstatite. Strict chemical definitions of each of the above parageneses, which is based primarily on the Mg# of olivine, clinopyroxene, and orthopyroxene, the Al 2 O 3 content of clinopyroxene and the CaO and Cr 2 O 3 content of garnet, is given by [42,[137][138][139].
Peridotitic substrates (mantle meta-peridotites), associated with peridotitic diamonds, likely formed in the hotter, Archean mantle due to extreme degrees of primary melt depletion associated with mantle-plume activity [30,[140][141][142]. However, the mechanisms of emplacement into the sub-cratonic lithosphere during collision and subduction remain unclear. Eclogitic substrates are thought to represent material derived from hydrothermal alteration, dehydration, and partial melting of subducted oceanic lithosphere [13,143,144]. This is supported by oxygen isotope compositions inconsistent with the mantle [13,145,146], sulfur (S) isotope compositions in accord altered oceanic crust and sediments exposed to the O 2 -poor Archean atmosphere [35,[147][148][149][150], and negative and positive Eu anomalies in garnet and clinopyroxene suggesting fractional crystallization processes in a relatively low pressure, crustal setting [144]. Several aspects regarding the formation of lithospheric diamonds and their inclusions are discussed in Sect. 3.3.1.
Like lithospheric diamonds, SDDs are commonly grouped based on inclusion paragenesis: meta-peridotitic (e.g., meta-harzburgitic) or meta-basaltic (and metapyroxenitic). The basis for this paragenetic division is given in Sect. 3.3.2 where mineral inclusions in SDDs are described in more detail. For now, we provide a general classification of SDDs (following [129]) based on the geologic setting and depth in which they form: Upper mantle and transition zone: these diamonds form in meta-basaltic-to-metapyroxenitic substrates at depths of 250-660 km and often contain inclusions of majoritic garnet and other silicates [6].
Lower mantle: these diamonds form in meta-peridotitic substrates and may contain inclusions of bridgmanite, CaSi-perovskite, and ferropericlase [6,88,92,151]. Only if inclusions of bridgmanite were observed, could one unequivocally assign a formation depth of > 660 km. If this is not the case in SDDs, distinguishing between transition zone and lower mantles origins is difficult. This is the case for the famous Cullinanlike, Large, Inclusion Poor, Pure, Irregular, and Resorbed (CLIPPIR) diamonds [54] which are interpreted to form between depths of 360-750 km in the deep metalsaturated mantle (see Sect. 4.3).
Approximately 98% of studied diamonds are lithospheric (2% are SDDs) and 64.8%, 32.8%, and 2.4% are peridotitic, eclogitic, and websteritic, respectively [42]. For peridotitic diamonds, 81% are harzburgitic, 18% are lherzolitic, and 1% are wehrlitic [134]. However, geophysical estimates by Garber [152] suggest that the cratonic lithosphere consists of ≤ 20% eclogite which is thus overrepresented by lithospheric diamonds. This may be due to selective incorporation of eclogite by the kimberlitic magma or more likely due to the relatively low preservation potential of peridotite compared to eclogite or other more complicated explanations as discussed in Chapter 6. Fluids associated with diamond formation and kimberlitic magmatism that are CO 2 -rich react with olivine to form magnesite to reduce the cohesivity of the rock and predispose peridotite xenoliths to disaggregation during kimberlite eruption [47,153,154]. Many other types of alteration (metasomatic oxidization and hydration, recrystallization, and re-equilibration) may affect the xenoliths during residence in the mantle and ascent to the surface, and in many cases, reliable identification of parental-rock type is impossible. For such cases, classification based on the host-rock type is useful. Lithospheric and sub-lithospheric diamonds are found in four principal rock types, following the recent nomenclature revisions of Pearson [155], they are as follows: [1] Kimberlites (or Group I kimberlites): ultramafic, potassic (K/Na > 1) igneous rocks that are rich in volatiles, particularly CO 2 (6.6 ± 3.3 wt% for n = 307, [155]), and contain primarily forsterite, pyrope, Cr-diopside, enstatite, phlogopite, chromite, serpentine, and carbonates. Isotopic compositions of Sr, Nd, Hf, and Pb suggest equilibration in the convecting mantle [156].
For the purposes of this review, we refer to such rocks as kimberlites, lamproites or lamprophyres, and in most cases as simply kimberlites to simplify description of magmatic and eruptive systems responsible for the transport of diamond to the surface. In general, kimberlitic, lamproitic, and lamprophyric deposits are highly texturally and mineralogically variable depending on what part of the deposit (e.g., crater-, diatreme-, and hypabyssal-facies) is exposed and thus being examined, i.e., the degree of exhumation and erosion of the kimberlite pipe. Approximately 30% of kimberlites are diamondiferous, significantly more common than lamproites and lamprophyres all of which are significantly younger (on average 45 Ma to 1.2 Ga, [26]) than the diamonds they host and the Archean cratons they intrude. The youngest known kimberlite pipe located in Igwisi, Tanzania, erupted~12,000 years ago [160].

Imperfections in natural diamond
Here, we define an imperfection in a hypothetical single crystal of diamond, D c , as any substitutional atoms in D c that are not carbon, any interstitial atoms in D c including carbon, any mineral, melt or fluid inclusion in D c , and/or any crystallographic feature of D c that is not strictly given by the space-group symmetry, Fd 3 m. Imperfections can be classified as intrinsic and extrinsic as follows: Intrinsic: imperfections related to site vacancies, edge dislocations, plastic deformations, or interstitial carbon atoms. Intrinsic imperfections do not involve atoms other than carbon.
Extrinsic: imperfections related to impurities (e.g., N, H, and B). Intrinsic and extrinsic imperfections influence the properties of diamond (Chapter 2) and can be grouped as point-defects and/or extended-defects. Point-defects describe imperfections that occur at a discrete location in the diamond crystal structure, typically displacing < 10 atoms (across 1 to 2 unit-cells) from their ideal positions in a perfect crystal of diamond. Examples of intrinsic point-defects in diamond include site vacancies (V) and interstitial carbon (C i ) atoms that occupy a position off-center with respect to the lattice point. The most common extrinsic point defect is single substitutional nitrogen (N s ) or interstitial nitrogen (N i ). Extended defects describe imperfections that consist of larger scale aggregates of impurities vacancies and/or edge dislocations. Lattice dislocations and loops (see below) are common examples of intrinsic extended-defects. The most common type of extrinsic extended-defect are platelets, planar features that consist of complex aggregations of N s and C i around vacancies.
Inclusions of any mineral, melt, or fluid may be regarded as a type of extrinsic extended-defect. However, as they may form under conditions unrelated to that of diamond formation and independent from crystallographic influence of the diamond (e.g., protogenetic inclusions), we discuss inclusions in a separate Sect. 3.3. There are an extremely large number of different imperfections in diamond, and in the following sections, we focus on those that are the most informative with regards to diamond genesis, growth, and residence in the mantle.

FTIR spectroscopy: vacancy-nitrogen-hydrogen point-defects
Selected vacancy-nitrogen-hydrogen defects in diamond are listed in Table 1. Most of these defects have yet to be recognized in experiment, others have been described by DFT calculations but have simulated intensities below of the detection limit of any current spectroscopic techniques and/or are obscured by other more intense peaks (e.g., [173,177]). The most common and well-understood defect families observed in natural [177]. Absorption of IR light occurs at frequencies associated with C-H, and N-H stretching and bending vibrations, each of which may correspond to several different vibrational modes. Additional properties, such as isotopic composition (e.g., 14 N vs. 15 N), charge state, and the quantum spin-state, influences the position of peaks in the IR. Detailed descriptions of N-, H-, and vacancy-related defects and their corresponding signal observed in the IR are given by [131,[178][179][180].
The concentrations of the most common defects: C-centers (N s ), A-centers (N 2 ), and B-centers (VN 4 ) can be calculated, specifically the concentration of A-and Bcenters ([N A ] and [N B ]) and %B to group diamonds according to the Type classification system (Sect. 2.2.4). However, most natural diamonds contain detectable amounts of both A-and B-centers, and thus, the corresponding signal in the one-phonon region of the FTIR spectrum must be deconvoluted before %B can be calculated, and a Table 1 Selected vacancy-nitrogen-hydrogen defects that may occur in diamond Although not specified in this table, each defect may occur in neutral, positive, and negative charge states, different quantum spin-states and with different isotopic compositions, all of which may shift the position (cm −1 ) of corresponding band in the FTIR spectrum (e.g., [177]). This table does not contain all possible vacancy-nitrogen-hydrogen defects; readers are referred to [131,177,180] and references therein for description of other defects Fig. 14 The FTIR spectra of a Type IaB diamond showing absorption in the one-phonon, N-region due to A-and B-centers, the platelet peak at~1378 cm −1 (D-center), absorption in the two-phonon region due to intrinsic lattice vibrations, the 3017 cm −1 (H' peak) and 1405 cm −1 peaks due to C-H stretching and bending, respectively, associated with the VN 3 H defect, and the 3236 cm −1 peak which has yet to be definitively assigned a defect configuration but may be due to N-H stretching N3-center, three N s around a vacancy, in which H forms a C-H bond to passivate the dangling bonds of the fourth C [187]. It follows that trapping of a H atom by an N3center (VN 3 ) may be the dominant mechanism by which VN 3 H defects are produced [180]. However, it has been shown both theoretically and experimentally (in HPHT) diamonds that VNH defects may trap A-centers (N 2 ) to produce VN 3 H defects [187,190]. Regardless of the aggregation sequence responsible for the formation of VN 3 H defects, it is evident that H plays an important role in quenching N aggregation. This relationship has been evaluated in detail through comparison of peak intensities and defect concentrations by [180,187,191,192].
Other relatively intense peaks in the IR that have been assigned to H-related defects include the 2786 cm −1 and 3236 cm −1 peaks (Fig. 14). The intensity of the 2786 cm −1 peak shows some correlation with the 3107 cm −1 peak and has been attributed to an overtone of the 1405 cm −1 C-H bending mode of the VN 3 H defect [180,187]. Other peaks observed at 4167 cm −1 , 4496 cm −1 , 5555 cm −1 , 5880 cm −1 , and 6070 cm −1 also have intensities that correlate with that of the 3107 cm −1 peak and are attributed to various overtone and combination bands of the VN 3 H defect. The 3236 cm −1 peak is most commonly observed in Type IaB diamonds and often not observed in diamonds with low N content [178]. The intensity of the 3236 cm −1 peak shows no correlation with the intensity of the 3107 cm −1 peak and thus has been attributed to N-H stretching as opposed to C-H stretching [179,180,188]. If this was the case, one would also expect a N-H bending mode at~1600 cm −1 which has not been observed. An inverse correlation between the intensity of the 3236 cm −1 peak and the D-center (platelet) peak has been observed and Gu et al. [173] suggests that this peak may be associated with N-H stretching associated with a platelet-centered VN 4 H defect. This defect would form by H trapping by a B-center (VN 4 ) and has important implications for platelets acting as H reservoirs in diamond as discussed in Sect. 3.2.

N and H impurities and vacancies: extended-defects
All extended-defects are inherently related to combinations of intrinsic and extrinsic point-defects. For example, irradiation can eject a C atom from its site to produce C i and vacancies which migrate and coalesce with increasing mantle residence time and temperature. These areas of aggregated point-defects (interstitials and vacancies) are relatively susceptible to plastic deformation (shear stress) that may result in mechanical twinning and edge dislocations depending on the temperature. In response to increasing shear stress, edge dislocations will propagate through the diamond structure ( Fig. 15a-c). Due to the cubic symmetry of diamond, two sets of dislocations may occur along [111] slip planes parallel to the octahedral face, shuffle and glides sets [193][194][195]. Shuffle and glide sets describe edge dislocations along planes in which C-C bonds of the same and different indices are broken, respectively ( Fig. 16) [196]. As is the case with N s and B s , dislocations involve breaking of C-C bonds and the formation of dangling bonds which may act to trap other impurities such as H. This structural description of dislocations in diamond masks a wealth of complexity and readers are referred to the above references for a more detailed description. Edge dislocations propagate and combine to form dislocation loops and mosaic networks   16 The two types of dislocation sets that commonly occur in diamond, the shuffle sets (along planes shown in green) and the glide sets (along planes shown in red) in which the C-C bonds of the same and different crystallographic indices are broken, respectively. Structure generated from ATOMS V6.4 with data from Straumanis and Aka, [89] which are characteristic internal features in Type IIa and IIb diamonds, often observed via CL spectroscopy (e.g., [53,113]). In Type I diamonds, N impurities increase the yield strength of diamond and primary growth features are often preserved even where there is evidence of plastic deformation.
Platelets are the most common type of extended-defect observed in natural diamond and consist of thin regions of C i , N s and vacancies that occur in the [100] plane [180,197,198]; however, recent works suggests that platelets consist primarily of C i [199]. Platelets, commonly referred to as the D-center, give rise to a characteristic peak in the IR (the B' peak) observed at 1358-1378 cm −1 (Fig. 14) [135] where the exact peak position and width varies as a function of platelet shape (short or elongate), size (diameter), and density [192,200]. For example, Goss et al. [197] showed that increasing platelet size is accompanied by a downward frequency shift of the B' peak. It is now widely accepted that platelet formation is related to the production and accumulation of C i as a biproduct of various N-aggregation sequences. As described in Sect. 2.2.4, N s defects (C-centers) aggregate with other N s defects and vacancies to produce A-and B-centers. The first and simplest mechanisms proposed for production of C i and platelets involves the combination of two A-centers (N 2 ) (1) to form a Bcenter (VN 4 ) as follows: Additional aggregation sequences [ (2) and (3)] may produce C i but requires one to assume A-centers migrate as dissociated N s (rather than N 2 ) as suggested by [201,202], e.g., N 2 →N s + N s (dissociation of A-center) However, ab-initio calculations by Goss et al. [197] suggest that these aggregation processes alone are not sufficiently fast to produce platelets observed in some experiments and propose a growth mechanism related to the formation of dislocations and subsequent production of mobile VN 2 defects that combine with A-centers to produce C i . FTIR studies suggest that these aggregation sequences [and (2)] are responsible for platelet formation and growth as there is a linear correlation between the intensity of the B-center peak (and [N B ]) and the B' peak. Such diamonds are referred to as regular diamonds [199]. In other diamonds, referred to as irregular diamonds, there is minimal correlation between the intensity of the B-center and B' peaks as platelets degrade with increasing residence time and temperature [199]. Speich et al. [192,199] have shown that degradation proceeds according to a first-order rate equation and have proposed methods to calculate the degree of platelet degradation and annealing temperature of irregular diamond during residence in the mantle. Platelet compositions with considerable H contents have been observed [173], particularly in degraded platelets, suggesting that H incorporation may quench platelet growth [180]. By taking into account the aggregation and degradation rate of platelets and the [N B ] of the diamond, methods to reconstruct the thermal history of the diamond during residency in the mantle have been developed [192,199].

Mineral, fluid, and melt inclusions
Inclusions are the most informative imperfection in natural diamond. Since the earliest rigorous analytical work on inclusions in the 1960s (e.g., [135,203]), the study of inclusions in diamond have driven continued development of models for diamond formation from C-bearing fluids in cratonic mantle keels and the deeper convecting mantle [6,42,88,134,[204][205][206].
Approximately 1% of diamonds contain minerals inclusions [42] which can be grouped as protogenetic, syngenetic, and epigenetic based on whether they crystallized before, during, or after diamond formation, respectively. For decades, classical With continued growth, diamond faces grow at unequal rates and begin to partially surround mineral grains until they are completely entrapped by the diamond. Note how mineral inclusions have the same morphology as the diamond and retain their original crystallographic orientation (shown with blue lines in each inclusion). Modified from Angel et al. [219] thermobarometric work was conducted under the assumption that all inclusions grew syngenetically with their host diamond (formed from the same chemical reaction) and, in some cases, were later altered by epigenetic processes [108]. This was assumed based on the encapsulating diamond imposing its morphology on the inclusion minerals which typically appear octahedral and cubo-octahedral regardless of their crystal symmetry [207][208][209].
However, relatively recently, it was shown that inclusions may be protogenetic and form before their host diamond [210,211], such inclusions represent minerals that comprise mantle lithologies into which diamond-forming fluids infiltrate and react (metasomatize) and are included during diamond growth, as shown in Fig. 17. This has been shown for several common inclusion minerals with diamond-like morphologies such as olivine, clinopyroxene, garnet, and magnesiochromite [210,[212][213][214][215][216]. These types of analyses often rely on Crystallographic Orientation Relationships (CORs), which describe the orientation relationship between (1) individual inclusion minerals, and (2) between the inclusion minerals and their host mineral (diamond) [217][218][219]. The above description masks a wealth of complexity, and in some cases, syngenetic inclusions may form from distinct processes (different chemical reactions) than their host diamonds (i.e., synchronous inclusions, [212]). Accurate determination of syngenesis or protogenesis has major implications for interpretations of geobarometric and geochronological data and readers are referred to the following references for a detailed explanation of syngenetic, protogenetic, and epigenetic inclusions [210,212,215,219,220].

Mineral inclusions in lithospheric diamonds
Most mineral inclusions in lithospheric diamonds appear as cubo-octahedral, range in size from nanometers to hundreds of microns and may occur as single crystals and/or crystal aggregates and/or polycrystalline material of the same or different minerals. Inclusions often act as loci for plastic or brittle deformation (Sect. 3.2), often observed as graphitized fractures around inclusions.
The most common mineral inclusions in lithospheric diamond are in accord with the mineralogical bulk composition of the upper mantle, largely meta-peridotitic (i.e., pyrolitic). However, inspection of Fig. 2 reveals major differences between the abundance of mineral inclusions in lithospheric diamond (as listed above) and those expected for the dominant upper mantle lithologies (e.g., meta-harzburgitic, meta-lherzolitic, and meta-basaltic rocks) some of which may be due to the fact that inclusions in diamonds of all parageneses are included above. When considering individual parageneses, the abundance of some mineral inclusions in diamond are in accord with the predicted abundance of that mineral for the corresponding mantle lithology. For example,~12% of observed inclusions in peridotitic (harzburgitic, lherzolitic, and wehrlitic) diamonds are orthopyroxene [42] and primitive mantle peridotite is predicted to comprise~15% orthopyroxene (Fig. 2); this small overestimation may be explained by the instability of orthopyroxene in peridotitic assemblages at depths > 280 km [70]. For other inclusions, namely olivine and garnet, observed abundances of inclusions in diamonds of known paragenesis are significantly different than those predicted for the corresponding mantle lithology. For example, 62% and 16% of inclusions are garnet and olivine in peridotitic diamonds, respectively [42], and primitive mantle peridotite is predicted to comprise~17% garnet and~58% olivine (Fig. 2) [70]. If one assumes entrapment of minerals by diamond occurs randomly, then peridotitic diamond-forming substrates must be enriched in Cr-spinel, sulphides, and garnet and depleted in olivine. Otherwise, one must assume the mode by which minerals are entrapped by diamond is non-random. Common mineral inclusions in peridotitic diamonds are shown in Fig. 18.
As discussed in Sect. 2.2.5, peridotitic diamond substrates are typically meltdepleted and eclogitic diamond substrates are sourced from slab environments in subduction settings. A deeper understanding is gleaned by comparison of majorand trace-element data from inclusions in diamond, representative of the diamond substrate, and mantle xenoliths, representative of the cratonic lithospheric mantle. Analysis of garnet peridotite xenoliths shows the proportion of harzburgite to lherzolite is 18:82%, effectively the inverse determined from peridotitic inclusions in diamonds suggesting that harzburgite may serve as the primary diamond substrate in the cratonic mantle [134]. In general, major-element geochemistry of Mg/Fe 2+ in olivine, Cr/Al and Na/Ti enrichment in garnet, cpx and opx, and REE trends of peridotitic substrates and mantle xenoliths supports the preference for diamond formation in melt-depleted peridotitic (harzburgitic) substrates followed by episodic metasomatic events involving re-enrichment of depleted peridotitic substrates and diamond formation. Moreover, similar Mg# (Mg/[Mg + Fe 2+ ] × 100) of olivine inclusions in  [214] diamond and outside the diamond in the associated xenolith suggests that the diamond substrate is the primary control on the crystal chemistry of inclusions in diamond as opposed to the diamond-forming fluid or melt [134].
Eclogitic diamonds are characterized by predominately garnet and clinopyroxene inclusions ( Fig. 19) with the addition of orthopyroxene for websteritic diamonds [42]. In general, picritic-basaltic rocks from subducted oceanic crust are considered the dominant protolith of diamondiferous eclogite xenoliths [13,222] and evidence for this from inclusions in diamond is discussed in Sect. 2.2.5. The lithologic diversity of the subducted oceanic crust is reflected in the variable major-and trace-element compositions of inclusions observed in eclogitic diamonds. In general, eclogitic mineral assemblages are representative of the more mafic Archean-to-early Proterozoic oceanic crust. The Na, Ca, and Mg# of garnet inclusions in eclogitic diamonds suggest involvement of different igneous protoliths, such as clinopyroxene gabbroic cumulates (High Ca and Mg# in garnets) and olivine (± orthopyroxene) cumulates, and extrusive protoliths, such as ocean-floor basalts (low Ca garnets) [13,42,143,223]. The bulk  [42,224,225]. For detailed descriptions of the major-and trace-element and isotopic compositions and petrogenetic interpretations of individual mineral inclusions in lithospheric diamonds, readers are referred to [42,134,144].
To explain this discrepancy, Lorenzon et al. [237] analyzed 57 ferropericlase inclusions in 37 diamonds and showed that there are two populations of ferropericlase, one relatively Fe-rich and Mg-poor (Mg# < 0.70) (magnesiowustite), and a second that is Fe-poor and Mg-rich (Mg# > 0.80). Evaluation of the Crystallographic Orientation Relations (CORs) (see Sect. 3.3) of these inclusions showed that low Mg# ferropericlase have a non-random orientation with respect the host diamond indicating a potential syngenetic origin (co-crystallization of ferropericlase and diamond). Higher Mg# ferropericlase have a random crystallographic orientation with respect to the host diamond indicating a protogenetic origin (crystallization before diamond formation). To explain these observations, Lorenzon et al. [237] proposed a dual origin for ferropericlase involving potentially syngenetic growth of low Mg# (Fe-rich) ferropericlase and diamond in the upper mantle where diamond formation is likely associated with fluids derived from subducted slab materials and entrapment of protogenetic (pre-existing) high Mg# ferropericlase in the lower mantle. An upper mantle, subduction-related origin for low Mg# ferropericlase is supported by the Fe 3+ contents and calculated f O2 (based on Fe 3+ /[Fe 2+ + Fe 3+ ]) of some low Mg# ferropericlase inclusions suggestive of an oxidized subducted material reacting with reduced metaperidotites to produce magnesiowustite and diamond [3,68,[238][239][240].
Inclusions of stoichiometry, ABO 3 are most often observed as breyite (CaSiO 3 ) (Fig. 20b) and enstatite (MgSiO 3 ) (Fig. 20a) but may also be observed as perovskite (CaTiO 3 ) and wollastonite (CaSiO 3 ) [246]. In general, CaSiO 3 inclusions fall into two distinct groups, with high and low-Ti contents [6] but show significant differences in terms of MgO, Al 2 O 3 , and FeO contents compared to CaSiO 3 inclusions from experiments [3, 6, 234-236, 247, 248]. MgSiO 3 inclusions are often grouped based on their Al 2 O 3 content where low-Al MgSiO 3 inclusions have low CaO contents and high Mg# consistent with depleted lithologies such as harzburgite. The majorelement chemistry of high-Al MgSiO 3 is not as well constrained but low Mg# in some inclusions is consistent with bridgmanites synthesized from meta-basaltic assemblages [67,151,249].

Fluid and melt inclusions
The study of microinclusions of fluid in diamonds, particularly fibrous diamonds, has tremendously improved our understanding of how diamonds form by metasomatic reactions ( [52] and references therein). Metasomatism of mantle rock by carbonand H 2 O-bearing (C-O-H) fluids reduces (or in some cases oxidizes) carbon species in solution to form diamond [45,277]. These diamonds may encapsulate fluids as inclusions and provide the only direct means to sample diamond-forming mediums from the deep Earth.
Caution must be used when differentiating fluids and melts related to (1) inclusions in diamond, which are analyzed at surface temperatures and (2) diamond formation, where fluids and melts are modeled at P/T and f O2 conditions in the diamond stability field. With respect to (1), fluids inclusions, most often observed in fibrous diamonds, retain fluid-like properties from the moment of diamond formation to eruption at the surface. In contrast, melt inclusions are described based on their properties during diamond formation, and are not stable under decreased P/T conditions where they solidify to form glassy inclusions (e.g., [278]). With respect to (2), differentiating fluids and melts is much more complex and is dependent on P, T, f O2 and the composition of the fluid or melt. Here, only a brief description of fluid inclusions in diamond is provided and a more detailed description of how diamonds form from C-O-H fluids is given in Chapter 4.
Fluid inclusions are typically ≤ 1 μm (on average 0.2-0.5 μm) in size and fully fibrous cuboid diamonds or fibrous coats on monocrystalline cores may contain millions of inclusions resulting in a translucent or cloudy appearance [52]. In some cases, fluid inclusions result in strain, evidenced from highly birefringent fibrous zones [52]. At the time of diamond formation, fluid inclusions consist of supersolidus melts or high-density supercritical fluids (HDFs) [279,280] until the temperature decreases during ascent of the diamond to the surface where HDFs separate into low-density fluids (LDFs) and mineral solutes [48,206,281]. C-O-H-HDFs and melts of similar composition (e.g., high-Mg carbonatitic HDFs and carbonate melts, see below) likely form in similar environments where HDFs represent (1) relatively low volume, lowdegree partial melts or (2) residual fluids produced through fractional crystallization of parental melts [52]. At pressures conducive to SDD formation, H 2 O-rich HDFs will likely exceed their second critical endpoint (the solidus termination in P/T space, [279,280]) and have a high dissolved silicate content and thus are best described as melts rather than fluids [6,280,[282][283][284][285][286]. In simplistic terms, LDFs are supercritical aqueous fluids with a lower dissolved solute (silicate) load than HDFs which include supersolidus melts and dense supercritical aqueous fluids above the second critical endpoint [52] where such fluids have a higher H 2 O to dissolved solute ratio than melts.
In general, C-O-H fluids may contain H 2 O, CO 2 , CO 3 , HCO 3 , CH 4 , and/or H 2 and the dense supercritical fluid-HDFs inferred from analysis of fluid inclusions in fibrous diamond are divided into four groups based on their major-element compositions [52,287]: Melt-HDFs are similarly classified based on similar compositional groups (see Sect. 4.2.2) as associated fluid and melt-HDFs with similar compositions likely form in the same geologic setting and/or from the same parental melt as described above.
A compositional join is observed between silicic and low-Mg carbonatitic HDFs (Fig. 21) which have been interpreted to form from hydrous, carbonated eclogites based on HDF inclusions in eclogitic mineral inclusions and experimental H 2 O-CO 2 -eclogitic melts [288,289]. Elezar et al. [289] and Dvir et al. [290] showed that the position of such melts along the silicic to low-Mg carbonatitic array is likely a function of the H 2 O/CO 2 ratio of the eclogitic source rock. Other interpretations involve dissolution of carbonates in H 2 O-and K 2 O-rich silicic melts [287], or the dissolution of silicates into carbonatitic melts [291], both with increasing temperature. High-Mg carbonatitic HDFs are associated with melting of carbonated peridotitic sources [287,292]. Weiss et al. [52,292] suggest both high-Mg carbonatitic HDFs and kimberlitic melts form from low-and high-degree partial melting of carbonated peridotites, respectively. Saline HDFs are interpreted to form from seawater-altered subducted slabs based on Sr isotopes signatures, high Cl-contents, low K/Cl ratios, positive Sr and Eu anomalies, and low 3 He/ 4 He ratios [48,51,[293][294][295][296]. Weiss et al. [287] suggest that percolation of carbonated peridotite by saline HDFs may produce high-Mg HDFs in which the required trace-element load is supplied by the saline HDFs.
Major and trace elements in HDFs may de-couple as (1)(2)(3)(4) show two distinct traceelement patterns: (1) a highly fractionated trace-element pattern enriched in LILE and LREE and depleted in HFSE and alkali elements consistent continental crust and  [51], respectively. The low-Mg and silicic compositions form a continuous array (red arrow) in accord with fluids and melts produced by experiment in hydrous eclogite + carbonate systems [287,288,292]. Modified from Shirey et al. [48], data from diamonds from DeBeers-Pool, Koingnaas, Kankan, Koffiefontein, Brazil, Diavik and Siberia, Jwaneng, Panda, Wawa and can be retrieved from Shirey et al. [48] (2) a relatively smooth trace-element pattern slightly depleted in LILE and LREE consistent oceanic basalt [297,298]. Such trace-element patterns are also observed in kimberlites, and oceanic and continental volcanic rocks. These observations in addition to the enrichment in incompatible trace elements and volatiles observed in HDFs and their connection with subduction processes suggest that they play important roles in cycling and transport of H, C, and other volatiles into the deep Earth [52].
HDFs provide a distinct mechanism for the formation of both fibrous and non-fibrous (monocrystalline) diamonds compared to other C-O-H fluids such as low-density H 2 O-rich fluids. For example, the alteration of depleted peridotitic and eclogitic garnets by HDFs produces sinusoidal REE patterns like those observed in harzburgitic garnet inclusions in monocrystalline diamonds (see Sect. 5.2) [42,51]. Some compositional correlations have been made between core-to-rim HDF profiles in fibrous diamonds and saline and carbonatitic HDF inclusions in octahedral, monocrystalline diamond, and macles (twins) [299][300][301]. Further evidence for involvement of fluids during diamond growth is hydrous silicic fluid rims (1-5 μm-thick films of Si(OH) 4 and Si 2 O(OH) 6 fluids) around inclusions (Fig. 22) observed in > 90 lithospheric diamonds from the Siberian and Kaapvaal cratons [302] and from the Voorspoed mine [246] and in several sub-lithospheric diamonds from Juina (Brazil) and Kankan (Guinea) [274]. Several other studies on fluid inclusions in monocrystalline diamonds have been conducted [303][304][305]; however, the results of such studies are mostly speculative due to difficulties constraining the timing of fluid entrapment (e.g., due to fractures permitting post-entrapment re-equilibration) and analytical limitations related to the extremely small size of most fluid inclusions. The above observations suggest that HDFs play a crucial role in the formation of both fibrous and monocrystalline lithospheric and sub-lithospheric diamonds.

Diamond formation and growth
In this chapter, we describe the fundamental physical and chemical mechanisms for diamond formation and growth. As covering all aspects of natural diamond formation would require an entire book, we focus on the diamond-forming fluids and the associated metasomatic (redox) reactions related to diamond nucleation and growth. Moreover, we evaluate how changing P, T, and redox (f O2 ) conditions influence the composition and carbon speciation of C-O-H fluids for different redox reactions responsible for diamond nucleation and growth.
As the validity of all experimental (and to some extent, theoretical) models for diamond growth are completely reliant on accurately replicating the P/T conditions of natural diamond formation, a brief description of chemical and elastic thermobarometric practices for diamond are given in the following section followed by a synopsis of the major results produced by applying these methods to mineral inclusions in diamond.

Geothermobarometry of diamond
Geothermobarometry of diamond involves the determination of temperatures and pressures at which diamonds form, geothermometry and geobarometry refer to determinations of temperature and pressure, respectively. To determine the depth of diamond formation, one must rely on its mineral inclusions as, at present, there are no associated methods that are applicable to pure inclusion-free diamond. For an inclusion-free diamond, only residence temperature, T res , in the mantle can be determined based on N-aggregation state (Sect. 3.1.1). We emphasize that residence temperature is different than formation temperature, where determination of the latter is the principal goal of diamond thermobarometry. For specific mineral inclusions, different chemical and/or elastic geothermobarometric methods can be applied to the diamond-inclusion system, a synopsis of these methods is given in the following sections.

Chemical geothermobarometry
Chemical geothermobarometry involves calculation of pressures and/or temperatures at which a single-mineral inclusion or a pair of mineral inclusions is/are in chemical equilibrium based on their measured chemical composition. However, to apply this approach to mineral inclusions within a diamond, we must assume that the inclusions formed simultaneously and from the same reaction (a syngenetic inclusion, see Sect. 3.3) that formed the diamond host in the mantle. Otherwise, in the case of a nonsynchronous formation between diamond and its mineral inclusions, we must assume that when the host entraps its pre-existing mineral inclusions (a protogenetic inclusion, see Sect. 3.3), the chemical equilibrium is reset and the inclusion and diamond reflect the same crystallization conditions. Following Nimis [4], we report the most commonly used thermometers and barometers used to derive temperature and pressures based on: (1) The exchange of a chemical component between two inclusion minerals in equilibrium-mineral-pair thermobarometry. (2) The measured contents of a given element in a single mineral-monomineral thermobarometry. Pressure and temperature determination assumes that both (1) and (2) behave according to a specified (experimentally derived) calibration curve [4]. Examples of mineral-pair thermometers include the clinopyroxene-orthopyroxene thermometer based on exchange of an enstatite component (MgSiO 3 ) between both pyroxenes, the Ni-in-garnet thermometer based on the Ni content in garnet and olivine in equilibrium and the Fe 2+ -Mg thermometers based on the distribution of Fe 2+ and Mg between two associated mineral inclusions, such as olivine-garnet, clinopyroxene-garnet, and orthopyroxene-garnet. Monomineral thermometers are particularly useful when the number or size of diamond inclusions is limited and include the Ca-in-orthopyroxene thermometer [306], the single-clinopyroxene thermometer [4], and the Al-in-olivine thermometer [307,308]. Examples of mineral-pair barometers include the orthopyroxene-garnet barometer based on the Al content of orthopyroxene in equilibrium with garnet and the clinopyroxene-garnet barometer based on the equilibrium reaction grossular + pyrope <-> diopside + Ca-Tschermak [309][310][311]. Examples of monomineral barometers include the Cr-in-clinopyroxene barometer based on the Cr content in diopside in equilibrium with garnet [5,312], and the Cr-in-garnet barometer based on the Cr content of garnet in equilibrium with orthopyroxene and spinel [313,314].

Elastic geobarometry
The elastic geobarometric method is an alternative approach to chemical geobarometry as described above and has been reviewed in detail by Angel et al. [219]. This method relies on differences in the thermoelastic properties (mainly thermal expansivity and compressibility, [315]) of the diamond host and its mineral inclusions [316]. Thus, this approach is not reliant on the chemical composition on mineral inclusions or aspects of their chemical equilibrium. The pressure at which the diamond entraps a mineral inclusion is defined as the entrapment pressure (P trap ) and corresponds to the depth of diamond formation [219,220]. When the diamond is erupted to the Earth's surface, its volume expands but, at the same time, the inclusion within it tends to expand more (i.e., diamond has an extremely low compressibility and coefficient of thermal expansion, Sect. 2.1.3). It follows that that inclusion minerals remain under pressure after the diamond has reached the surface; this is called the residual pressure or internal pressure (P inc ). Once P inc is determined, one can use the thermoelastic properties of the diamond and the inclusion mineral to back calculate the pressure at which the diamond entrapped the inclusion (P trap ) [219,220]. In principle, the elastic geobarometric method can be applied to all possible inclusion minerals found in diamond, regardless of their chemical composition which strongly constrains the applicability of chemical barometric methods. It follows that use of elastic barometric methods may drastically increase the number of inclusion-bearing diamonds that are suitable targets for geobarometric analysis.
As mentioned above, elastic geobarometry requires that P inc be derived; this can be done using three different methods: (1) measurement of the unit-cell volume of the inclusion mineral at room temperature and pressure before and after it is extracted from the diamond host (this can be done by X-ray diffraction techniques); using the bulk modulus, K 0T , of the inclusion mineral (if known), the difference in unit-cell volume can be used to calculate P inc [220]; (2) measurement of the Raman band shift of the inclusion (using Raman spectroscopy) before and after it is extracted from the diamond host; this approach requires that the Raman band shift as a function of pressure is known (e.g., [317].); and (3) evaluation of the strain-induced birefringence in natural diamonds, although not commonly used, this technique is also very reliable (e.g., [318]).
Once P inc is determined using one of the above three methods and if the thermoelastic parameters of the inclusion and diamond are known, one can calculate P trap for a given temperature, this is most easily done using the free downloadable software EosFit-Pinc (see [319]). By plotting P trap at different temperatures, one can construct what is called an isomeke [219], a curved line in P-T space that provides the depth of formation of the diamond-inclusion pair at any reference temperature.
The elastic geobarometric approach is based on a few assumptions and involves several complexities that should be considered. For example, if the diamond-host system did not behave elastically, and instead plastically (or elasto-plastically), P inc and the resulting P trap will be strongly affected. In addition, the elasticity of minerals is often anisotropic (elasticity changes as a function of the direction of the applied stress), the effect of these features on the elastic geobarometric method is not fully understood but may produce erroneously low P trap values. As a result, calculated P trap is often reported as a minimum pressure at which the studied inclusion was entrapped (e.g., [87]).

Results from geobarometric analysis of mineral inclusions in diamond
In general, lithospheric diamonds form in mantle keel environments at depths of 120-200 km (average depth of 175 ± 15 km) and at an average temperature of 1160 ± 100°C and pressure of 5-6 GPa [5,43,85]. Stachel and Luth [45] report an average temperature of 1140°C and pressures of 5 GPa for diamond formation based on garnetolivine thermometry. Nimis [4] compiled thermobarometric data for inclusions (using a single-clinopyroxene barometer and Ni-in-garnet thermometer) in lithospheric diamond and showed an average depth of formation of 190 km at pressures of~6 GPa and temperatures of~1200°C.
Sub-lithospheric diamonds form below the sub-continental lithospheric mantle (SCLM) in the convecting mantle at depths of~300-800 km and at average temperatures and pressures of 1200-1500°C and 9-11 GPa [6,7,86,87]. However, the majority of SDDs form around the transition zone at 410-660 km [88]. Based on analysis of high-pressure mineral inclusions, such as periclase, jeffbenite, breyite, corundum, and SiO 2 , Harte [70] suggests that environments around the transitionzone-lower mantle boundary at depths of 600-800 km may also be conducive to SDD formation. Much of the recent thermobarometric work on diamonds has focused on SDDs, and thus, in the following section, several examples of how the phase relations of inclusions in SDDs can be used to constrain the pressures, temperatures, and depths (and thus geologic settings) associated with formation of the inclusion (and in some cases the diamond) is given.
With respect to majoritic garnet, two different coupled substitution mechanisms produce compositions between end-member majorite, Mg 3 (MgSi)(SiO 4 ) 3 [241,242] and Na-majorite, (Na 2 Mg)Si 2 (SiO 4 ) 3 [243,244]. Such substitution mechanisms are pressure dependent, and thus, the formula contents (apfu) of majoritic garnet can be used a barometer [245,270,320,321]. Nimis [4] shows that many SDDs have depth estimates between 300 and 600 km which correspond to the depths at which subducted oceanic crust crosses its solidus (at 1100-1200°C) [6] to produce carbonated melt required for diamond formation [3,245,248]. Pressure estimations using the barometer of Thomson et al. [245] show a bimodal distribution at 7-10 GPa and 12-15 GPa [6]. Thomson et al. [245] show that most low-Cr majoritic garnet of meta-basaltic paragenesis comprises the higher pressure distribution and may represent a unique (deeper) environment of SDD formation compared to high-Cr garnets of meta-peridotitic paragenesis that comprise the lower pressure paragenesis and likely form in a shallower environment.
With respect to CaSiO 3 inclusions, single-phase inclusions of breyite are common in SDDs and have been observed in association with perovskite, (CaTiO 3 ); CaSi 2 O 5titanite; larnite, (Ca 2 SiO 4 ); merwinite, Ca 3 Mg(SiO 4 ) 2 ; chromite, (Fe,Mg)Cr 2 O 4 ; baddeleyite, ZrO 2 ; sulphides and Fe-Ni alloys [7,53,66,254,255,257,258,261,322]. As the phase relations in the CaSiO 3 system as a function of P, T, and Ti 4+ content are well understood, it is possible to model the P/T history of a diamond based on the position of the Ca(Si,Ti)O 3 inclusions along the CaSiO 3 -CaTiO 3 join. For example, end-member CaSiO 3 -perovskite is stable at pressures > 13-14 GPa and decomposes to larnite and CaSi 2 O 5 -titanite between 10 and 13 GPa, to breyite between 9 and 10 GPa (at 800-1700°C) and to wollastonite below 4-3 GPa (at 900-1500°C) [6]. When breyite is observed as composite inclusions with larnite and/or CaSi 2 O 5 -titanite, one can assume a formation pressure of~10 GPa (~300 km depth) [323]. Elastic barometric analysis of a breyite inclusion by Genzel et al. [7] indicates a minimum entrapment pressure of 9-10 GPa, at such pressures at ambient mantle temperature (1400-1500°C), breyite is not stable suggesting retrogression from CaSiO 3 -perovskite [7]. The case is much different for CaTiO 3 where Ti 4+ acts to reduce the stability of perovskite at high pressure, i.e., end-member CaTiO 3 is stable at pressures < 5 GPa [262]. In any case, phase transitions occurring over large pressure ranges, 3 to 22 GPa, and thus large depth ranges, have prompted work on mechanisms of transport in the mantle, such as convection, mantle plumes, and melt percolation [65,66,258,324,325]; this is discussed more in Sect. 5.3.1.
The stability of the MgSiO 3 polymorphs as a function of pressure and Al 2 O 3 content (mol. fraction) is well understood; thus, Al 2 O 3 content can be used as a barometer. Although the formation pressure of bridgmanite is strongly controlled by equilibration with intergrown phases (e.g., majoritic garnet, ferropericlase, and corundum), high-Al MgSiO 3 typically form at relatively higher pressures as opposed to low-Al MgSiO 3 [6]. As discussed in Sect. 3.3.2, breyite, and especially enstatite, may form as primary inclusion minerals at lower pressures compared to their perovskite-structured polymorphs. When such inclusion minerals are observed in SDDs with single-mineral barometers like majoritic garnet, one may make more precise estimations about the primary or secondary nature of breyite or enstatite inclusions. However, when observed with inclusions like ferropericlase that serve only as indirect barometers, more detailed work is required to constrain pressures of formation.
Another inclusion mineral that has received recent attention is jeffbenite (formerly known at TAPP, [326]), which has the same chemical composition as pyrope, Mg 3 Al 2 Si 3 O 12 [327,328]. It has been shown by experiment that primary Ti-rich jeffbenite may form at relatively high pressures (12-13 GPa) and temperatures (1400°C) at depths of 360-390 km [249]; however, of the 23 jeffbenite inclusions observed in diamond, none contain significant quantities of TiO 2 [328]. Inspection of the theoretical stability field of Ti-free, Mg end-member of jeffbenite, supports an origin for these inclusions related to regression of Al-rich bridgmanite [329] as this phase becomes unstable at pressures > 4 GPa at 500°C or > 2 GPa at 800°C [328].

Models for diamond formation and growth in the lithospheric mantle
Above, a brief description of the thermobarometric methods and associated results for the P/T and depth conditions of diamond and the inclusions they contain is given. Now, attention is turned to the physiochemical processes associated with the formation of diamonds in the mantle. In general, the solubility of carbon in mantle silicates and oxides is low and carbon is stored as mobile high-density fluids and melts until it is reduced to allow nucleation of diamond. We begin by discussing lithospheric diamonds as there is a wealth of data regarding the composition of reduced fluids in lithospheric diamonds and xenoliths [240,330]. For now, we refrain from specifying fluid or melt type (Sect. 3.3.3) (e.g., saline HDFs or carbonatitic melts) and, instead, assume the diamond-forming medium is simply a C-O-H fluid.
As discussed in Sect. 2.1, the stability of carbon as a function of P and T (Fig. 5) can be simply expressed as a phase transition from graphite to diamond with increasing pressure. The stability of diamond in the C-O system as a function of P, T, and f O2 is constrained by the reactions (4) and (5) C diamond ↔ C graphite (4) However, diamond-forming (C-O-H) fluids contain H and, thus, the stability of different diamond-forming reactions [e.g. (6)] is reliant on the oxidation state of the mantle substrates (e.g., meta-peridotites), through which they percolate and needs to be considered.
To do this, the redox speciation of C-O-H fluids and the reduction potential (i.e., f O2 ) of lithospheric mantle peridotites and eclogites at different P/T conditions must be evaluated. Akin to chemical thermobarometric techniques, oxy-thermobarometery of xenoliths has provided information about the redox conditions in cratonic mantle lithologies [44,240,331,332] and can be used to estimate the equilibrium f O2 for mineral assemblages observed in mantle xenoliths (e.g., the garnet-olivine-orthopyroxene (GOO) oxy-thermobarometer, [333]). These f O2 values are typically calculated against the buffer reaction (7) and reported at f O2 -FMQ [47,334] fayalite (3Fe 2 SiO 4 ) The FMQ buffer reaction constrains the upper bound of f O2 in the lithospheric mantle at a given P and T which has f O2 -FMQ = − 1.5 to − 3.5 at P/T conditions across the diamond stability field [48], as indicated by the average f O2 -FMQ from mantle xenoliths from depths of 140-180 km [335]. The lower bound of f O2 is constrained by the IW buffer reaction (8) The f O2 conditions above the IW buffer are not adequate to reduce sufficient FeO to allow for Fe alloys to precipitate from Fe-silicates, such that the f O2 falls below the IW buffer curve. As f O2 fluctuates between the FMQ and IW buffers as a function of P/T, the stability of C-species in C-O-H fluids changes. At f O2 -FMQ < − 2, CH 4 is stable and predicted to be the dominant C-H species at f O2 -FMQ = − 4.5 [48,336,337].
The f O2 of the cratonic mantle at P/T conditions in the diamond stability field is shown to be sufficiently reducing to form diamond by reduction of C-O-H fluids. However, metasomatic reactions involving CO 2 -bearing fluids and olivine-bearing substrates (i.e., peridotites) add complexity to this picture.
The EMOD equilibrium plots at f O2 -FMQ = − 0.5 to − 2.0 [47] and data from garnet-peridotite xenoliths suggests the cratonic mantle plots on the reducing side of the EMOD buffer [21,49] where magnesite (MgCO 3 ) and CO 2 (at higher temperatures) are unstable, and the formation of diamond is favored. This is simply shown in Fig. 23, where log-f O2 is plotted as a function of temperature. Above the EMOD buffer, diamond is unstable and magnesite reacts with enstatite to produce CO 2 with increasing temperature (Fig. 23) as shown in reaction (10) enstatiteMg 2 Si 2 O 6 + magnesite 2MgCO 3 = forsterite 2Mg 2 SiO 4 + CO 2 . (10) At relatively higher temperatures (compared to the EMOD buffer reaction), the DCO buffer reaction (11) represents the upper bound of f O2 in the P/T stability of diamond (Fig. 23) The DCO is within 1 log-f O2 of the EMOD buffer, and at f O2 above the DCO buffer, reaction (10) proceeds and diamond is unstable. At f O2 below the DCO buffer, CO 2 in fluids is reduced to form diamond at appropriate pressures.

(12)
The DCDD plots approximately one log-f O2 above the EMOD buffer curve suggesting that the f O2 stability field of diamond is wider in eclogitic substrates compared to peridotitic substrates over the same P/T conditions [47,338,340].
In peridotitic or eclogitic substrates, one may envision a hypothetical C-O-H fluid composition (L eq ) in equilibrium with a peridotitic mantle rock. Infiltration of this substrate by a compositionally different CO 2 -rich fluid (L d1 ) that is significantly more oxidizing than L eq will result in diamond precipitation via CO 2 reduction (reaction (8)). Infiltration of this substrate by a CH 4 -rich fluid that is significantly more reducing than L eq will result in diamond precipitation via CH 4 oxidation [reaction (9)]. Such reactions are called wall-rock-buffered redox reactions as oxygen exchange is mediated by Fe 2+ -Fe 3+ in Fe-silicates and oxides of the peridotitic or eclogitic substrate (wallrock) [19,21,48].

Isochemical precipitation of diamond from C-O-H fluids
In the previous section, wall-rock-buffered redox reactions, that constrain the f O2 stability field in which diamond form, are explained. Such reactions involve the oxidation or reduction of C-species in C-O-H fluids, as these reactions occur above the IW buffer, Ni-Fe alloys are unstable, and Fe 2+/3+ in silicates and oxides is free to mediate the oxidation or reduction of C-species. However, the majority (~56%) of the cratonic mantle substrate is depleted harzburgite and dunite [48], which have relatively low Fe 2+ contents significantly reducing the buffering capacity of such substrates and the degree to which C-species are reduces to form diamond. Luth and Stachel [21] showed that wall-rock-buffering by mantle peridotites is not sufficient to generate significant quantities of diamond by demonstrating that f O2 can be shifted from the EMOD to the IW buffer by removing < 50 ppm O 2 from the peridotitic substrate. Consequently, it is likely that the f O2 of some depleted cratonic substrates may be fluid-buffered (see below). This may explain the observed discrepancy between f O2 -FMQ of lithospheric mantle peridotites under diamond-stable P/T conditions in experiment and the f O2 -FMQ of mantle xenoliths which would be representative of the last fluid they were in contact with [47].
As f O2 crosses DCO buffer curve, CO 2 reduces to form diamond and O 2 and the H 2 O content of the residual C-O-H fluids increases. At 2 log-f O2 below the DCO, ( f O2 -FMQ close to that of peridotitic substrate at diamond-stable P/T), the fluid approaches the H 2 O-maximum, and the residual fluid is nearly pure H 2 O (90-99 mol%) with minimal CO 2 and CH 4 content [45]. In near H 2 O-maximum fluids, diamond has a large solubility change with temperature, and as P/T conditions of such fluids decrease during ascent along a mantle geotherm, isochemical precipitation of diamond may occur (reaction (13)) at f O2 -FMQ slightly below the EMOD buffer (− 1.5 to − 2.4) [47] If these near H 2 O-maximum subsolidus fluids enter more reducing conditions where f O2 -FMQ ≤ -3, the following reaction (14) is more likely [134,341]: These reactions are redox-neutral and do not require oxygen exchange with Fesilicates, Fe-oxides, and/or sulphides. Assuming an adequate (or frequent) fluid supply and low fluid-rock ratios, reaction (13) can produce significant quantities of diamond (> 5 carats/ton) [134], significantly more than peridotitic or eclogitic wall-rockbuffered reactions. This is supported by HPHT experiments where H 2 O-rich fluids are shown to promote diamond growth [342,343]. Diamond precipitation from near H 2 O-maximum fluids can only occur in depleted harzburgites (or dunites) as dilution from partial melting in other substrates, with relatively lower solidus temperatures, may increase diamond solubility and prevent nucleation. Such processes have been attributed to the common association of lithospheric diamond and harzburgitic garnet [45].
Reactions (13) and (14) may also result from simple mixing of mantle-derived, reducing CH 4 -C 2 H 6 -rich fluids and subduction-derived, oxidizing CO 2 -CO 3 -rich fluids. However, such mixing processes would result in extreme C isotope fluctuations across internal growth zones, a feature not observed in most lithospheric diamonds which show consistent (or gradational) C isotope compositions across growth zones [48].

C-speciation and composition of C-O-H high-density fluids and melts
In the previous section, we have treated C-O-H fluids generically and not specified how particular fluid states (e.g., melts vs high-density fluids) or compositions (e.g., saline vs. silicic HDFs) influence metasomatic processes and diamond formation at conditions with variable P, T, and f O2 . The speciation of C in C-O-H fluids can be predicted as a function of log-f O2 -FMQ as shown in Fig. 24 where it is shown that fluids dominated by C-H (e.g., CH 4 , C 2 H 6 , H 2 ) and C-O (e.g., CO 2 ) are in equilibrium with diamond at relatively low and high f O2 , respectively. In Fig. 24, note the relatively wide range of log-f O2 -FMQ where fluids near the H 2 O-maximum (indicated by m in Fig. 24) are in equilibrium with diamond. This range (− 3 to − 2 log-f O2 -FMQ) overlaps with the f O2 -FMQ of cratonic mantle peridotites on the reducing side of the EMOD buffer.
As discussed in Sect. 3.3.3, LDFs may be defined as supercritical fluids and HDFs include both supersolidus melts and supercritical fluids with a higher dissolved solute (silicate) load compared to LDFs and a composition that is H 2 O-rich compared to melts. In the following section, we follow the description of LDFs and HDFs given in Sect. 3.3.3 but for the purposes of simplicity refer to both low-density and high-density fluids as simply fluids unless specification is warranted.
In most cases, the inclusions in diamond, particularly garnet, have a much more depleted character than cratonic peridotitic xenoliths and xenocrysts suggesting fluid or melt metasomatism is involved in diamond formation. Differentiating fluid and melt metasomatism is typically done using the incompatible trace-element composition of garnets [313,344,345]. The relatively high Zr/Y contents of most harzburgitic garnet suggest fluid metasomatism, and low Zr/Y values for most lherzolitic garnet suggest melt metasomatism and subsequent re-enrichment of the substrate. This has been attributed to harzburgite and lherzolite substrates forming at conditions below and above their hydrous solidus, respectively [45,229]. It follows that only harzburgitic The IW (iron-wustite) and EMOD (plotted as E) are shown using red circles. Modified from Wood, [180] after Stachel and Luth,[45] substrates are permeable to fluid, as melt percolation will lead to equilibration and crystallization at depths < 180 km, and that suprasolidus lherzolitic substrates are permeable to melts [134].
One can now further constrain the type of fluid associated with metasomatism of peridotitic (e.g., harzburgitic) substrates. Such fluids are unlikely to have significant CO 2 contents (unless at f O2 above the EMOD buffer where diamond is unstable) due to the buffering reaction (10) [134,346]. For efficient fluid interconnectivity and subsequent fluid percolation through olivine cumulates, the fluid-rock dihedral wetting angle, θ , must be below a threshold value, i.e.,θ ≤ 60°in an ideal, isotropic system [347][348][349]. The dihedral wetting angle describes the angle between two different but adjacent solid (mineral)-fluid interfaces; at a triple grain boundary, there is complete fluid interconnectivity and the rock is completely wetted (has a high wetness) where θ = 0° [350]. The relatively high CO 2 -olivine and CH 4 -olivine dihedral wetting angles (θ = 80-90°for a CO 2 -H 2 O where X CO2 = 0.9), [349]) may prevent fluid interconnectivity and flow of CO 2 -and CH 4 -rich fluids through peridotitic substrates at P/T conditions in the lithospheric mantle. In contrast, the H 2 O-olivine dihedral wetting angle decreases with increasing pressure to θ = 48°and 42°at pressures of 3 and 5 GPa, respectively, at 1000°C [351]. Capizzi [352] shows that the dihedral wetting angle of carbonatitic liquids in mantle peridotites increases with H 2 O content up to θ = 50°. The above description is representative of an ideal isotropic, completely crystalline substrate. However, it is likely that some degree of partial melting occurs upon infiltration of diamond-forming fluids into peridotitic substrates. Here, even extremely low degrees of melt can significantly affect θ and thus the degree to which such fluids can percolate through the substrate [353]. Mu and Faul [354] show that for partially molten dunites (melt contents of 0.3-6.8%), additional variables, such as grain size, pore morphology, and melt content, control the distribution of melt and grain boundary wetness. As discussed in Sect. 4.2.1, fluids in peridotitic and eclogitic substrates are likely near the H 2 O-maximum (90-99 mol%) at f O2 conditions in the diamond stability field. The addition of dissolved alkali species in H 2 O-fluids does not significantly affect the dihedral wetting angle [349,355]. The solubility of incompatible trace element in aqueous fluids is significantly larger than in CO 2 -and CH 4 -rich fluids [134,356], and percolation of aqueous fluids with high concentrations of incompatible elements may explain the commonly observed re-enrichment (LREE enrichment) of melt-depleted peridotitic substrates, i.e., sinusoidal REE trends in harzburgitic garnets (see Sect. 5.2). Rather counterintuitively, the above discussion suggests fluids associated with metasomatism of peridotitic, specifically harzburgitic, substrates are H 2 O-rich and have low contents of CO 2 and CH 4 (~2% at the H 2 O-maximum). Such aqueous fluids at P/T conditions in the diamond stability field probably have a large concentration of incompatible elements and are thus best described as high-density fluids (HDFs) [51,52].
Evidence from xenoliths and diamond inclusions for melt metasomatism of peridotitic, specifically lherzolitic, substrates points to four primary melt compositions; carbonate, silico-carbonate, silicic, and hydrous melts [134]; however, other types of melts, such as metallic, sulfide, and saline melts, have been identified [52]. In general, carbonated melts form in localized regions at high f O2 ; it follows that temporary perturbations in the redox conditions of the reducing lithospheric mantle are required. Carbonated melts may form from upwelling of metasomatized mantle rock into conditions of higher f O2 and subsequent redox melting [68,134]. Carbonated melts may also form from melting of oceanic crust, although significant melt cannot be generated at depths < 400 km, below the anhydrous solidus of carbonated eclogite, incorporation of slab-derived fluids may permit melting at shallower levels. Moreover, in the hotter Archean and Paleoproterozoic lithospheric mantle, partial melting of carbonated subducted crust and subsequent metasomatism of the lithospheric mantle likely occurred in shallower levels [357]. Mantle metasomatism by silicic and silicocarbonate melts has been inferred from orthopyroxene-rich peridotitic xenoliths that form from Si enrichment of peridotitic substrates via hydrous melts [358,359] or mafic melts [360]. Other studies attribute silicic melt metasomatism to the formation of large-igneous provinces and associated plume magmatism [361].
The fluid/melt compositions associated with metasomatism of eclogitic (or pyroxenitic) substrates are more difficult to constrain as most mantle eclogites are LREE-depleted and show no evidence of re-enrichment via metasomatism by diamond-forming fluids or melts (as described for peridotitic substrates above). However, Na-rich garnet and K-rich clinopyroxene inclusions have been attributed to diamond formation from saline HDFs (see Sect. 3.3.3) [134]. This is supported by the observation of saline HDF inclusions in eclogite [293,362] and Na-and K-rich omphacite and saline HDF inclusions in associated eclogitic diamonds [295]. Based on the f O2 of eclogitic xenoliths, it is likely these HDFs are near the H 2 O-maximum and form in subduction-related environments where they can dissolve and incorporate different C-species [338,363]. In such environments, diamond formation may be fluidbuffered and oxidizing (e.g., CO 2 -bearing fluid) and reducing (e.g., CH 4 -bearing fluid) HDFs may precipitate diamond upon mixing via isochemical (oxygen-conserving) redox reactions (Sect. 4.2.1) [21,341]. Of course, this does not preclude wall-rockbuffered reactions, such as diamond precipitation via oxidation of CH 4 and reduction of Fe 3+ in the eclogitic substrate [364].
Some high-Mg eclogites show evidence (LREE enrichment) of metasomatism by silico-carbonate or kimberlitic melts [365]. Such melts are in equilibrium with eclogite and diamond over wider ranges of f O2 compared to peridotite. Moreover, diamond in eclogite is stable at higher f O2 compared to peridotite [338], and thus, transport of C and precipitation of diamond associated with metasomatism of eclogites may occur over large distances and a wide range of conditions [366]. This may explain the overrepresentation of diamonds with eclogitic paragenesis compared to the estimated eclogite content of the lithosphere [134,367]. In general, clear evidence for metasomatism of eclogites is rare, and when observed, it is unique from that in peridotite. This may be due to the limited trace-element data for inclusions in eclogitic diamond or from overprinting of trace-element metasomatic signatures of eclogitic xenoliths by interaction with kimberlitic HDFs or melts [134].

Models for formation and growth of super-deep diamonds
At around the depth at the base of the upper mantle (~410 km), f O2 is likely close to, or at the IW buffer [reaction (8)] where Ni-Fe alloys begin to precipitate out of high-pressure Fe-silicates [47]. Based on estimated upper mantle Fe/O contents, Frost and McCammon [240] predict that this process may begin at shallower depths of2 50 km. However, contradictory evidence is shown with high Fe 3+ / Fe ratios in majoritic garnet (20% Fe 3+ at 10 GPa, [368]) and wadsleyite (2% Fe 3+ , [369]) from the transition zone and in CaSiO 3 -perovskite (> 50% Fe 3+ , [370]) from the lower mantle, all of which in equilibrium with Ni-Fe alloy at f O2 around the IW buffer. If one assumes that the estimated bulk Fe/O content (Fe 3+ / Fe ratio of the upper mantle is < 2%, [369,371]) is consistent across the entire mantle due to convection, how could the relatively small Fe 3+ budget of the transition zone and lower mantle support assemblages of Fe 3+ -rich silicates and Ni-Fe-rich alloys in equilibrium? The additional Fe 3+ required is produced through the disproportionation reaction producing Ni-Fe alloy (Fe 0 metal); 3Fe 2+ O = Fe 3+ 2 O 3 + Fe 0 [47,240,330,370]. This reaction is driven by the increasing solubility of Fe 3+ in silicates with increasing pressure and is responsible for the nearly 1 wt% Fe 0 metal comprising the lower mantle [68,368,372]. This reaction also constrains f O2 in the base of the upper mantle, the transition zone and the lower mantle to values close to or at the IW buffer and thus to conditions sufficiently reducing to allow diamond formation from C-bearing fluids or melts [48,68].
The stability of diamond in the transition zone and lower mantle is assessed by Rohrbach and Schmidt, [68] and Stagno et al. [373] who propose reaction (15) as a high-pressure version of the EMOD buffer Although this buffer reaction plots 2-3 log-f O2 above the IW buffer, it assumes homogenous Fe/O contents throughout the transition zone and lower mantle and does not take into account the counteractive effect of FeO disproportionation on f O2 . In fact, carbon at P/T conditions in the transition zone and lower mantle is extremely soluble in Ni-Fe alloys (~2 wt% C), metallic Fe-rich liquids (~6 wt% C) and/or Fe-carbides (e.g., Fe 3 C and Fe 7 C 3 ) [374]. Thus, at f O2 conditions at or below the IW buffer, the majority of C in the deep mantle, which occurs in relatively low concentrations (50-200 ppm) compared to the lithospheric mantle, may be stored as Fe-metal or liquid in disequilibrium with diamond [48]. This is evidenced from Fe-metal and sulphide melt inclusions in many sub-lithospheric diamonds [53,113,375]. For example, Kaminsky and Wirth [376] observed Fe-carbides (Fe 3 C, Fe 2 C, and Fe 23 C 6 ) in association with Fe-metal in diamonds from the Juina area.
Models for SDD formation are in some ways analogous to the redox-and fluidbuffered models for lithospheric diamond formation, albeit the SDD-forming media and substrates are significantly different. The Redox-Freezing model [68] for SDD formation involves the production of carbonated melts from subducted material, and their migration into the reducing, Fe-metal-saturated peridotites where C-species are reduced (via oxidation of FeO) to form diamond [248,377]. Metasomatism of Fe-metal-rich peridotites by carbonated melts in HPHT experiments have produced periclase with variable composition (along the Mg-Fe join) and Ca-majoritic garnet and Ca(Si,Ti)O 3 -perovskite with compositions in accord with inclusions in SDDs [248,377]. Moreover, the wide range of light carbon isotope values, the heavy oxygen isotopic composition and high Fe 3+ content of majoritic garnet inclusions suggest involvement of subducted crustal rocks [66,151,[378][379][380]. However, major-and traceelement data of SDDs suggest several different melting processes and subsequent melt compositions from which diamonds may precipitate.
Barometry of majoritic garnet in SDDs shows that the majority of SDDs form between depths of 300-600 km in the transition zone where slab subduction stagnates [381,382] and undergoes partial melting [6]. Such SDDs often contain Cr-poor majoritic garnet and Ti-rich CaSiO3 inclusions in accord with low-degree partial melts of oceanic crust and a meta-basaltic assemblage [3,66,248,258]. Here, melting likely occurs at 1100-1200°C and at pressure of 13-18 GPa [6,245]. Subduction systems may also transport diamonds from shallower environments in the upper mantle to higher pressure environments in the base of the upper mantle and transition zone. Lorenzon et al. [274] argue that zirconia + coesite and ringwoodite inclusions in a diamond formed as products of prograde phase transitions of zircon or reidite (ZrSiO 4 ) and olivine or wadsleyite, respectively, during transport of the host diamond from the upper mantle potentially hundreds of km to depths possibly > 610 km.
The observation of exsolved brucite and magnesioferrite in ferropericlase inclusions, hydrous inclusion minerals such as ice VII [61], a hydrous Al-silicate called phase EGG [AlSiO 3 (OH)] [383], hydrous ringwoodite inclusions (e.g., 1.5 wt% H 2 O, [276]), and hydrous fluid films around inclusions [92,274,302] point to the involvement of H 2 O-rich fluids and melts across the transition zone and shallow lower mantle where SDDs form (e.g., [92]). Fluid phases rich in H 2 O and CH 4 are theoretically stable in the deep reducing peridotitic mantle but unlikely to exist in any significant quantity due to the H-storage capacity of the deep upper mantle and transition zone (e.g., [384]). Instead, H 2 O may be transported to the deep mantle in cold subducting slabs where H 2 O is stored in dense-magnesium-silicate (DHMS) phases, which can contain 5-10 wt% H 2 O (e.g., [385]). Upon stagnation and heating on the slab in the transition zone, DHMS phases may breakdown to form wadsleyite or ringwoodite and residual H 2 O-rich fluid [6,133]. Such fluids may be carbonated from melting of the slab (or percolation within the slab) and would thus precipitate diamond upon migration through the surrounding peridotitic substrate. Here, melting of the cold slab, at transition zone pressures, would occur at 1200-1300°C where the predicted mineral assemblage is ringwoodite, akimotoite, bridgmanite, ferropericlase, and Ca-perovskite [133,386], the latter may be observed (as retrogressed breyite) in association with ringwoodite inclusions in diamond [276].
Based on several high-pressure mineral inclusions, Harte [70] suggests environments at depths of 600-800 km at the transition zone-lower mantle boundary may also be conducive to SDD formation. The CLIPPIR diamonds and diamonds from the Collier-4 kimberlites [378] have been shown to form in this region and have extremely variable carbon isotope compositions; δ 13 C = − 26.9 to − 3.8‰ and δ 13 C = − 26 to − 8‰, respectively [6]. This suggests formation from carbonated melts from subducted oceanic crust. The CLIPPIR diamonds contain composite Fe-Ni-S-C-rich inclusions of the carbide mineral, cohenite ((Fe, Ni) 3 C), Ni-Fe alloys, Fe-sulphides, Fe-Croxides, and Fe-phosphates [54] some of which are also observed in Type IIb diamonds [53,113]. Fe-Ni-Cr-S-rich metallic inclusions are interpreted as melt inclusions [53] perhaps produced through metasomatism and partial melting of Fe-metal-saturated peridotites associated with deep-seated subducted slabs. Moreover, CH 4 -H 2 fluid films observed in SDDs may have exsolved from metallic Fe-rich melt inclusions during decompression.
In general, our understanding of the redox reactions responsible for SDD formation is lacking compared lithospheric diamonds. This is largely due to a paucity of representative materials, SDDs are relatively rare and those with mineral and melt inclusions suitable for study, even more so. However, recent experimental work has provided several interesting results regarding the stability of different oxidized and reduced forms or carbon at P/T conditions of the deep lower mantle (see [387,388]).

Models for the aqueous speciation of metasomatic, diamond-forming fluids
Until now, and in much of the current literature, models for the speciation of C-bearing molecules and other dissolved solutes (e.g., K 2 O and Na 2 O in diamond-forming fluids (see Sect. 3.3.3) are rather simplistic. Although extremely useful and informative (as shown above), such models assume C-bearing species are for the most part, neutral dissolved gases (e.g., CO 2 and CH 4 ) and that diamond-forming reactions behave according to simple redox reactions. In recent years, detailed thermodynamic modeling (e.g., the DEW model, [389,390]) based on the aqueous solubilities of upper mantle lithologies and the mineralogical components therein (e.g., peridotite and eclogite), has shown that diamond-forming fluids may contain a much wider variety of mineral solutes, ionic species, and metal complexes [391] than previously known. Moreover, such works have shown that diamond-forming reactions may be more complicated than the standard redox controlled reactions as described above. Sverjensky and Huang [392] use models of mantle fluids containing ions to show that diamonds may form during water-rock interactions due to fluctuations in pH at relatively constant redox conditions (f O2 ). For example, these authors show that metasomatism and dissolution of the clinopyroxene (NaAlSi 2 O 6 ) and garnet (Mg 3 Al 2 Si 3 O 12 ) components of an eclogitic substrate may produce Mg-rich carbonates (MgCO 3 ) and H + , (reactions 16 and 17) thus lowering the pH of the system into the diamond stability field, such that diamond can precipitate via dissolution of MgCO 3 (reaction 18) at relatively constant logf O2 In general, experimental fluid compositions after metasomatic reactions with silicate mantle lithologies (e.g., eclogite and peridotite) are in good agreement with siliceous fluid inclusions observed in diamond (e.g., [392]). Several C-bearing species have been proposed based on the results of the DEW model that are not typically considered in most redox reactions, such as HCO 3 − and CO 3 2− and other organic carbon species such as HCOO − , HCOOH 0 , CH 3 COO − , CH 3 COOH 0 , and CH 3 CH 2 COO − [391] which have been proposed to react with H + in acidic solutions during metasomatism to produce diamond and water [392] (e.g., reactions 19 and 20) Similar studies modeling reactions between eclogitic fluids and peridotitic substrates (e.g., [393]) have shown that discrete reactions can form a wide variety of silicate minerals typically attributed to eclogitic, websteric, and peridotitic parageneses. It follows that a suite of different mineral inclusions in a single diamond may form syngenetically from the same metasomatic event that resulted in the precipitation of the host diamond. Above we have provided only a simplified synopsis of the work that has been done modeling the aqueous chemistry of diamond-forming fluids at mantle conditions and readers are referred to the work of D.A. Sverjensky and F. Huang (e.g., [389][390][391][392][393]) for more detailed explanations.

Mantle geodynamics of carbon through geologic time
Thus far, we have focused primarily on imperfections in diamonds and how they can be used to elucidate aspects of diamond formation from different mediums (e.g., fluids and melts) in different substrates (e.g., mantle peridotite and eclogite). Now, attention is turned to larger scale aspects of mantle geodynamics through geologic time as inferred from the study of imperfections in natural diamond. Here, recent, and more notable works, focused on (1) the extent to which C is recycled between crustal and mantle reservoirs, (2) the mechanisms and speciation associated with C transport in the mantle, and (3) the relation between the C and N isotopic composition of diamond (and diamond inclusions) and potential source reservoirs (e.g., [129]). We begin by evaluating the structural and compositional evolution of the mantle though geologic time based on the geochronology of diamond and associated temporal trends in the chemical (major and trace elements) and isotopic composition of mineral inclusions.

Geochronological methods and the age of diamonds
Accurate determination of the formation age of diamond is crucial to understand how the mechanisms and geologic settings of diamond formation have evolved through time. Diamonds are uniquely capable of capturing samples of the deep Earth through time, as far back as 3.5 Gya and thus may be used to reconstruct the geologic history of the mantle and Earth processes associated with diamond formation.
In general, geochronology (i.e., radiometric dating) is used to determine the age (or date) of inclusions by measuring the degree to which a parent nuclide, with a known decay constant (λ) (or half-life (t 1/2 )), has radioactively decayed to its daughter nuclide(s). For example, 187 Re decays to 187 Os according to λ = 1.6689 ± 0.0031 × 10 -11 a −1 [394] and t 1/2 = 0.693/λ [71]. Parent and daughter nuclides fractionate by differential partitioning into different mineral and fluid phases via diffusion and one must assume that a calculated crystallization (formation) age reflects the time that elapsed during fractionation until diffusion stopped and the isotopic system was closed. In the case of diamond, which does not contain sufficient concentrations of radiogenic elements, such as Sm, Nd, U, Pb, Re, and Os suitable for age dating (e.g., half-life of C is only 5730 years), one must rely on inclusions. In ideal cases, mineral inclusions crystallize at temperatures (at or above their closure temperature) high enough to isotopically homogenize the system (e.g., crystals ± residual melt). After diamond crystallization and encapsulation of a mineral inclusion, a rapid temperature decrease quenches the isotopic distribution among phases, such that the geochronometer is set. The surrounding diamond prevents further isotopic fractionation, and the mineral inclusion can be dated to determine the crystallization age of the diamond. The above description represents the simplest case, dating of diamonds is often much more complex and involves calculation of different types of ages using different geochronological methods (e.g., model vs. isochron ages, see [71,221]) that may reflect the age of different geologic events distinct from diamond crystallization such as the crystallization of protogenetic mineral inclusions. However, ambiguous diamond formation ages are often supported by supplementary geochronological data from other diamonds or xenoliths associated with the same deposit (kimberlite pipe). For example, Bulanova et al. [66] dated a SDD from the Collier-4 kimberlite at 107 ± 7 Ma, although this date is only 14 Mya older than the host kimberlite, which may seem unrealistic, the N-aggregation state of associated diamonds suggests relatively short mantle residence times (< 10 Mya at 1500°C) supporting this diamond formation age [66,71]. For a detailed review of the geochronological methods and associated analytical techniques used for dating diamonds, readers are referred to [71].
Lithospheric diamonds have formed throughout much of Earth's history recording ages as old as 3.3-3.5 Ga (Diavik Mine, Slave Craton) and 3.5 Ga (Panda kimberlite, Ekati mine, Slave Craton) [23][24][25] and are usually significantly older than their host kimberlites which have average ages of 45 Ma to 1.2 Ga [26], suggesting prolonged mantle residence times. In contrast, SDDs appear to be Mesoproterozoic or younger and, in some cases, may be transported to the surface soon after formation as shown by Bulanova et al. [66] above. However, conclusions based on the ages of SDDs lack statistical meaning compared to those based on lithospheric diamonds as SDDs with inclusions of appropriate size and composition for dating are exceedingly rare; currently, there are only four Re-Os and Sm-Nd model ages and two U-Pb ages for SDDs [71]. Nevertheless, such diamonds have provided crucial information about the sources and recycling of C in the transition zone and lower mantle which is discussed briefly below.

Evolution of the Archean and Proterozoic lithospheric mantle
Age dating of lithospheric diamonds that formed in Archean and Proterozoic peridotitic (specifically harzburgitic) and eclogitic substrates have provided much information about how cratonic nuclei and the underlying diamond factories (mantle keels) have formed and evolved over this geologic period. By linking diamonds with known ages and paragenesis to geologic settings, one can make inferences about the recycling of C-bearing volatiles and fluids in the mantle. Following [71], the ages for peridotitic and eclogitic diamonds and associated tectonic events are shown in Fig. 25.
Garnet has been particularly useful as it shows evidence of metasomatism in the form of REE patterns [344,395,396] that are often consistent between garnets inside and outside of the diamond. Most harzburgitic and lherzolitic garnet inclusions in diamond, and those from cratonic peridotitic xenoliths, show sinusoidal chondrite-normalized (CN) REE patterns (Fig. 26) but may also show several types of non-sinusoidal patterns, such as V-shaped, normal, and abnormal patterns (see [134,229,344,395]). This sinusoidal, REE pattern is perhaps the most widely recognized feature of subcalcic garnets associated with diamond formation [137,144,345]. To   [134] explain these patterns, the early evolution of lithospheric mantle peridotites is characterized by two major events, (1) extensive primary chemical depletion via partial melting by upwelling mantle plumes and (2) re-fertilization and re-oxidation via interaction with enriched melts and fluids [42,[397][398][399][400]. Other hypotheses suggest that the sinusoidal REE trend in garnet is primary and formed upon recrystallization of a premetasomatism Archean lithospheric mantle composed of chromite-rich harzburgite [401].
The origin of eclogitic substrates is linked to the onset of Wilson cycles of plate tectonics at~3 Ga [29] after the formation of Paleo-Archean mantle keels and diamonds therein. The oldest eclogitic diamonds are~3 Ga, before which only peridotitic, specifically harzburgitic, diamonds are observed with formation ages of~3.5 to 3.0 Ga [29,47]. Eclogitic diamonds and associated xenoliths with ages of~3 Ga often show isotopic evidence for interaction with fluids produced in a subduction environment from crustal material. For example, the 2.9 Ga eclogitic diamonds from the Kimberley, Bobbejaan, Jwaneng, and Orapa localities [22,27,402] have been linked to collision and subduction processes associated with amalgamation of the Kaapvaal craton as they show isotopic evidence (e.g., S isotopes with atmospheric signatures) for the involvement of subducted oceanic lithosphere [71,149,150,403]. Shirey and Richardson [29] proposed that these 3 Ga eclogitic diamonds form due to continent collision and the subsequent incorporation of oceanic lithosphere and fluids into the cratonic mantle keel [24] and thus mark the onset of Earth's Wilson cycles. If one assumes that this is the case, processes by which Paleo-and early Meso-Archean mantle keels form must be distinct from that given by modern plate tectonics, although they likely involve localized subduction-like processes [36]. The most likely hypothesis for the formation of Paleo-and early Meso-Archean mantle keels involves the rise of mantle plumes and associated melt production resulting in melt-depleted peridotitic substrates characteristic of Archean mantle keels [24,79,140,142]. Here, primary melt depletion was likely facilitated by elevated Archean mantle temperatures (100-300°C higher than today) [404] and low FeO contents of cratonic peridotites have been used to support melting via mantle-plume upwelling [30,140,141]. This model is consistent with models for the formation of the Slave craton where the initial continental lithosphere was thickened by underplate melting due to mantle-plume upwelling [141], in accord with detrital chromite ages associated with komatiite magmatism in the Slave craton [405]. Komatiitic magmatism and other magmatic processes associated with the formation of large igneous provinces have been used to explain the observed Si (i.e., orthopyroxene) enrichment observed in cratonic peridotites, i.e., Si enrichment in the Kaapvaal craton has been attributed to the Ventersdorp large igneous province [406]. In general, the appearance of eclogitic diamonds at~3 Ga may represent a transition from dominantly vertical modes to horizontal modes of plate tectonics [71]. Vertical modes involve mantle-plume upwelling, underplating, and subsequent thickening of the lithospheric mantle, vertical tectonism, and internal igneous crustal differentiation [407][408][409][410]. Horizontal modes involve lateral accretion of oceanic lithosphere, horizontal tectonism, advective thickening of the lithospheric mantle, and external igneous crustal differentiation [29,79,411]. There is an enormous amount of work on the evolution of plate tectonics and associated processes, and there is evidence for subduction (or subduction-like processes), accretionary tectonics and continental margin magmatism in the Paleo-and Eoarchean and even Hadean (e.g., [412][413][414][415] [417,418], and 0.72 Ga [419], and are associated with enrichment of depleted lithospheric mantle peridotites by diamond-forming melts and fluids [45]. As discussed in Sect. 4.2.1, initially melt-depleted peridotitic substrates have a relatively low wall-rock-buffering capacity for carbonate reduction (and thus diamond production) via Fe 2+ oxidation. However, lherzolization may have introduced FeO to peridotitic lithologies [30] and thus increased the buffering capacity of such substrates. Evidence from enriched mantle xenoliths suggests that these melts had sufficiently high f O2 to re-oxidize regions of the depleted lithospheric mantle [19,44,46,398,420] which may have acted locally to decrease the depth at which lherzolitic diamonds would form via wall-rock-buffered redox precipitation. These melts likely produced pathways of re-oxidized and re-fertilized mantle peridotite which in turn would promote kimberlite eruption [46,419], and therefore, such melts may be described as proto-kimberlitic [48]. However, magmatic (and metasomatic) processes associated with proto-kimberlitic melts and lherzolitic diamond formation are usually distinct from those associated with kimberlite magmatism and eruption as evidenced by the large age differences between most lithospheric diamonds and their host kimberlites. It should be noted that although most lherzolitic diamonds formed in the Paleoproterozoic-Neoproterozoic, younger ages have been observed (e.g., Mesozoic lherzolitic diamond, [403]) and are associated with regions reworked by later tectonic events [146,361,421,422] or with post-Archean lithospheric mantle settings [423][424][425].

Recycling of carbon and associated geologic processes
Since the inception of The Deep Carbon Observatory (DCO) and The Diamonds and Mantle Geodynamics of Carbon (DMGC) consortium, much effort has been made to understand the geological processes that drive carbon recycling between the crust and mantle. Processes related to the formation of Archean mantle keels and the oldest3 .3-3.5 Ga diamonds represent the earliest traceable examples of carbon recycling in the mantle. The degree to which vertical and horizontal tectonics were operative in the Paleo-Archean and Eo-Archean is still debated (e.g., [426,427]), and thus, the specific mechanisms by which C was transported between the lithospheric mantle and crust during this period is not fully understood. Nevertheless, diamond research has advanced our understanding of how different aspects of the carbon cycle have changed over the last~3.5 Ga, specifically in Earth's early history when important geologic processes occurred, e.g., crustal growth and continent assembly, the onset of Wilson cycles, and major changes in atmospheric chemistry.
As outlined in Chapter 4, lithospheric diamonds form during periods of fluid infiltration into reducing substrates of lithospheric mantle keels; however, little attention has been given here to processes that control the migration and recycling of such fluids from subduction-related environments or the deep mantle to the mantle keel. The earliest traceable recycling of C (e.g., 3.3-3.5 Ga, [23][24][25]) related to peridotitic diamond formation is associated with the formation and subsequent metasomatism of the first cratonic blocks and associated mantle keels [27]. The onset of later subduction-related events, associated with the appearance of eclogitic diamonds (at~3 Ga, [29]) involved stabilization of cratons via subduction (of a dominantly horizontal mode), and incorporation of oceanic crust and subsequent underplating [27,402,[428][429][430][431] and likely involved more efficient recycling of C from crustal (surficial) sources.
In contrast, Proterozoic, lherzolitic diamonds are associated with metasomatic modification of the lithospheric mantle rather than formation (i.e., peridotitic diamonds) or stabilization (i.e., eclogitic diamonds) of mantle keels [432]. Lherzolitic metasomatism is inherently linked to recycling and migration of carbon-bearing fluids and melts and is not typically associated with subduction along cratonic margins. For example, the 719 ± 49 Ma lherzolitic diamonds [419] from the Victor Mine have been linked to rifting of the Rodinia supercontinent and subsequent migration of C-bearing fluids and/or melts into the lithospheric mantle of the Superior craton [71,304]. Although non-subduction-related metasomatic re-fertilization is characteristic of lherzolitic diamonds, in many cases, recycling of C-bearing fluids in the lithospheric mantle is driven by orogenic-and subduction-related processes around cratonic margins [71]. Continental collision and consequent orogenesis (and subduction) at the margins of cratonic nuclei have been linked to diamond formation through the production and introduction of diamond-forming fluids to the cratonic mantle [27,403] and thus represent a key process by which carbon is recycled. Notable examples include Proterozoic subduction processes along Kimberley craton associated with the 1580 ± 30 Ma [433] Argyle diamonds (Halls Creek orogen, [434]) and the 1426 ± 120 Ma [416] Ellendale diamonds (King Leopold orogen) where diamonds in both localities form in >2.9 Archean mantle substrates [71,416]. Similar processes are indicated by the 1.86 ± 0.19 Ga Diavik diamonds and associated eclogitic xenoliths [24,435] which have been linked to the Wopmay orogen along the Slave craton [436].

Speciation of carbon in the lithospheric mantle: C and N isotopes
The stable isotopic composition of C is expressed in delta notation (δ 13 C) and given as Here, δ 13 C is the deviation of the measured C isotope ratio ([ 13 C/ 12 C] sample ) compared to the C isotope ratio of an internal standard, typically the Vienna-Pee Dee Belemnite (VPDB) ([ 13 C/ 12 C] VPDB , where δ 13 C VPDB = 0‰). The isotopic composition of common impurities and mineral/fluid inclusions in diamond is calculated similarly, although many isotopic systems have been used to differentiate sources (or reservoirs) for diamond-forming fluids (e.g., [134] and references therein), we restrict our discussion here to C and N.
Accurate differentiation of potential carbon sources is often difficult as it requires that C and N isotope heterogeneity associated with different C and N sources is preserved and recorded during diamond formation. In many cases, the C and N source rocks undergo processes, such as high-T fractionation (e.g., [437]), metasomatism (i.e., partial melting or recrystallization), or mixing between different C/N reservoirs (e.g., recycled vs. primordial mantle reservoirs), these processes result in re-equilibration of C and N isotopes [47,129]. If this occurs before diamond formation, the recorded isotopic composition reflects a homogenized (mixed) source and the original isotopic composition is lost along with information about the original source of C and/or N. It has also been shown that diamond precipitation in both fluid-buffered systems and wall-rock-buffered systems (sects. 4.2 and 4.2.1) may induce C isotope Rayleigh fractionation (see [48,335,438]). Fortunately, diffusion of C (and to a lesser extent N) has been shown to occur at negligible rates at lithospheric mantle temperatures [439][440][441] and thus the distribution of C and N in diamond is representative of formation (and subsequent growth) rather than post-crystallization residence [45,129].
Stachel et al. [129] report a main mode of δ 13 C = − 5.1‰ for a Kernel density estimation using 4308 inclusion-bearing diamonds from around the world where the modes for most lithospheric diamonds and SDD groups are within δ 13 C = − 5.1 ± 0.2‰ (Fig. 27). Howell et al. [37] report a similar value of − 5 ± 2‰ for 908 δ 13 C measurements made on 144 fragments of peridotitic and eclogitic diamonds with formation ages of 3.5-1.4 Ga and 3.0-1.0 Ga, respectively. These δ 13 C values are in accord Fig. 27 The δ 13 C values for peridotitic and eclogitic diamonds from the upper mantle, eclogitic diamonds from the transition zone, and diamonds from the lower mantle. Median values are shown with red lines, average values with red crosses, and the 25th to 75th percentile ranges for each diamond suite are shown with boxes where ranges are indicated with whiskers. Outliers are shown with small white and yellow circles for meta-basaltic and meta-peridotitic parageneses. The blue dashed lines indicate the isotopic composition of mantle C (δ 13 C = − 5.1‰) and similarities between the δ 13 C values of lithospheric peridotitic diamond and those from the lower mantle. From Stachel et al. [129] with the average C isotopic composition of the Earth's mantle based on carbonatites, kimberlite carbonates, and mantle xenoliths [437,442]. In general, these observations suggest that diamond-forming fluids generated in the mantle have remained constant with respect to C-speciation and f O2 since~3.5 Ga and that diamonds must grow in fluids with excess carbon [37] or in an environment that is continually resupplied with C-rich fluid. Moreover, in the case of eclogitic diamonds, significant isotopic homogenization must occur between C-bearing fluids derived from oceanic crust (with sedimentary and/or organic carbon of more negative δ 13 C) and mantle-derived fluids and/or melts. However, additional modes of δ 13 C at values significantly lower than − 5‰ are observed, particularly in eclogitic and websteritic diamonds (Fig. 27) [43,129], and may represent different fluid sources (with mantle and slab δ 13 C signatures) and/or varying degrees of isotopic fractionation as discussed below. The δ 15 N values of diamond from the same dataset of Stachel et al. [129] show much greater variation in comparison to δ 13 C,~2/3 of diamonds plot over the range δ 15 N = − 8.5 to + 1.5‰ with a mode at 3.5 ± 5‰ which is skewed to positive values with respect to the δ 15 N value of the mantle, − 5 ± 2‰ [443].
Overall, δ 13 C and δ 15 N range from − 41.4 to + 2.5‰ and − 39.4 to + 16.9‰, respectively, and several trends (covariations between δ 13 C and δ 15 N) have been recognized (see [129]) and interpreted based on processes involving kinetic and equilibrium isotopic fractionation models and fluid mixing models [129]. These models explain how preferential partitioning (given by isotope fractionation factors) of C and N isotopes changes as diamond growth proceeds and the isotopic composition of the diamond and residual fluid evolves. Such models may help one predict the C-speciation of diamond-forming fluids, and when coupled with geochronological and geochemical (paragenetic) information, allow one to infer evolutionary trends in C-speciation associated with different types of diamonds (e.g., peridotitic vs. eclogitic) through geologic time. As an example, consider the isochemical precipitation of diamond in fluid-buffered systems as described in Sect. 4.2.1, where diamond forms from fluids dominated by two C-species. Progressive growth of diamond from a CH 4 -CO 2 fluid will result in a core-to-rim δ 13 C enrichment of < 1‰ [48]. Precipitation of diamond from a fluid dominated by a single C-species in wall-rock-buffered systems (Sect. 4.2) may result in rimward δ 13 C enrichment or depletion when associated with CO 2 -or CH 4 -dominated fluids, respectively [48]. In general, Rayleigh fractionation will result in higher δ 13 C values of diamond precipitated from reducing (CH 4 -rich) fluids compared to a more oxidizing (CO 2 -rich) fluids if one assumes that the initial fluids are mantle-derived with mantle-like δ 13 C of~− 5‰. Such relations have been used to suggest that the δ 13 C of peridotitic diamonds (mode at − 5.2‰, [129]) must correspond to precipitation from fluids where CH 4 comprises ≥ 50% of the carbon species [48]. Stachel and Harris [43] attribute the relatively heavier δ 13 C values of lherzolitic diamonds, compared to other peridotitic diamonds, to involvement of carbonate fluids (δ 13 C− 5.5 to − 1.5‰) derived from subducted material. This observation may correspond to major changes in the Earths geodynamics during the Meso-and Neo-Archean where the transition of C recycling via partial melting and devolatilization of the mantle to C recycling via subduction occurred. It follows that diamond-forming fluids in the Eo-to Meso-Archean were likely more reducing and CH 4 -rich. Progressive introduction of subducted crustal material in the MesoArchean to Proterozoic likely resulted in more oxidizing (CO 2 -rich) fluids and diamond precipitation that occurred by reduction rather than oxidation [43,47].
In general, perturbations in the C and N isotopic composition, due to fractionation and post-crystallization metasomatism, often result in interpretations about the diamond-forming medium and/or substrate that have some degree of uncertainty. However, isotopic analysis of mineral inclusions, which are protected from processes that may overprint isotopic signatures of source materials, can provide less ambiguous information about the generation and recycling of C-bearing fluids and melts in the mantle.

Geodynamics of carbon in the sub-lithospheric mantle
Sub-lithospheric diamonds comprise~2% of studied diamonds [6,42,134] and the lack of geochronological work on SDDs (e.g., [71]) often results in ambiguous interpretations about the recycling of C in deep mantle. However, as no diamondiferous xenoliths with definitive origins in the transition zone or lower mantle have been discovered [6], SDDs are the only way to directly study the behavior and speciation of C-, N-, B-, and H-bearing fluids in the deep mantle and the extent to which associated geochemical cycles (e.g., deep C and H 2 O cycles) tap different recycled and primordial C reservoirs [58,59] in transition zone and lower mantle. Consequently, attention has recently turned to the study of SDDs and the inclusions they contain; in this section, we focus on the major hypotheses regarding the geodynamic processes associated with C recycling in base of the upper mantle, transition zone, and lower mantle.

Subduction-related recycling of carbon and SDD formation
Using different seismic methods, namely seismic tomography, the depth and extent of subduction zones, i.e., Wadati-Benioff zones, can be directly imaged. Consequently, it is well understood that downward motion of slabs may stagnate as deep as the transition zone (410-660 km) due to high P phase transitions and subsequent changes in buoyancy forces [381,382]. Here, slabs are displaced horizontally in the transition zone or at the boundary between the transition zone and lower mantle (~660 km) [48,444] where thermalization via conduction may allow slabs to descend slightly deeper into the shallow lower mantle. The depths at which slabs stagnate is complex and largely dependent on the slab geotherm and composition; in many cases, slabs may stagnate and/or undergo partial melting at much shallower depths [445] and have been associated with formation of some lithospheric diamonds. At depths between 410 and 660 km, slabs can undergo carbonated melting starting generally at temperatures of 1100-1200°C [6], although this is strongly dependent on slab geotherms and the H 2 O content during melting. The pooling of slab materials at~660 km likely forms major reservoirs for recycled C, N, S, and H 2 O [56]. As briefly discussed in Sect. 4.3, slab subduction and stagnation are the principal means by which H 2 O is recycled in the deep mantle [230,322,446].
There is a growing body of evidence that suggests some SDDs form from subducted material (e.g., [3,6,47,48,55,67,70,71,88,133,248,258,378,379,447]). In general, these formation models (described in the works cited above) involve the stagnation of subducting slabs in the transition zone and shallow lower mantle and subsequent melting of slab material (e.g., sediment, basalt, and peridotite) to produce smallvolume, potentially hydrous, and carbonate melts. Although the properties (density and f O2 ) of such melts vary as a function of P/T and composition, upon infiltration into the surrounding, highly reducing mantle rock, diamond may crystallize via Redox-Freezing (Sect. 4.2) [47,48,68]. It is important to note there is strong evidence for non-subduction-related formation of SDDs. For example, Gu et al. [92] provided evidence that polyphase inclusions of ringwoodite, ferropericlase, and low-Ni enstatite in diamond form at~660 km at pressures and temperatures of 23.5 GPa and 1650°C, respectively. These inclusions are accompanied by other hydrous phases and the source of H 2 O is attributed to the dehydration of ringwoodite upon disproportionation into bridgmanite and ferropericlase. These findings are associated with a potentially H 2 Orich environment at the transition zone-lower mantle boundary and thus preclude the requirement for introducing slab-derived materials to produce a diamond-forming medium.
Slab-derived, hydrous, carbonated melts or fluids are highly mobile and several processes by which C-bearing species are transported in the mantle, where diamond may eventually precipitate, have been hypothesized (e.g., [23,51,63,66].). Such fluids are likely aqueous, carbonated HDFs rich in dissolved Si and may infiltrate and metasomatize peridotite substrates within and outside of the slab to reduce C-species and produce diamond. However, many SDDs have several growth centers, complex internal zoning and irregular external morphologies (e.g., the CLIPPIR diamonds) [108] suggestive of multiple periods of diamond dissolution and re-growth. This observation in addition with composite phases interpreted as products of unmixing of high-P phases (e.g., [65,66,258]) suggests that some SDDs are transported hundreds of kilometers before incorporation in kimberlitic magma. One explanation involves cyclic Redox Freezing-Melting. Here, oxidized and C-rich regions of the mantle, metasomatized by diamond-forming fluids, undergo upwelling. Upon reaching a depth with the appropriate f O2 and C-content, diamond will oxidize (dissolve to some degree) to carbonate and lower the local solidus and redox melting will occur to produce another generation of carbonate melt [68,448]. Such melts may infiltrate reducing mantle peridotitic substrates and, once again, precipitate diamonds via redox freezing [47,48].
The relatively recent formation ages of SDDs may suggest that deep subduction and carbonated melt generation are required for not only SDD formation, but for the initiation of magmatic processes required to transport them toward the surface (e.g., kimberlite magmatism or mantle-plume upwelling). The absence of Archean SSDs (observed thus far) has helped elucidate the onset of modern-style deep subduction to at least the Mesoproterozoic [71] and provided a basis upon which one can begin to reconcile evidence for the onset of horizontal tectonics in the Meso-Archean (e.g., [29]) and its evolution toward modern-style tectonics in the Mesoproterozoic (e.g., [55]).

Carbon sources and mantle reservoirs: isotopic composition of SDDs
In general, meta-peridotitic and meta-basaltic SDDs show significant variability in δ 13 C values compared to lithospheric diamonds. As shown in Fig. 27, SDDs from the asthenosphere-transition zone show significantly lighter δ 13 C values; however, those with lower mantle origins show δ 13 C values close to that of peridotitic diamonds and mantle C.
Relatively light δ 13 C values for low-Cr majoritic garnet (δ 13 C = − 3 to − 25 ‰) compared to mantle carbon (δ 13 C = − 5 ± 2 ‰) in meta-basaltic SDDs have been attributed to diamond-forming fluids sourced from subducted, basaltic oceanic crust [66,69,151,437,[449][450][451][452] where the δ 13 C in the slab may vary from 0 ‰ for seawater C, to − 25 ‰ for organic sedimentary C [66,151,450]. An oceanic crustal source for meta-basaltic SDDs is supported by heavy δ 15 N values [69] relative to the primitive mantle, − 5 ± 2‰ [443] and heavy δ 18 O values in majoritic garnet and SiO 2 which points to incorporation of seawater in the subducted oceanic crust [378,379]. Meta-peridotitic SDDs show generally heavier δ 13 C values compared to meta-basaltic SDDs that often overlap with primitive mantle δ 13 C values; however, in many cases, major-and trace-element analyses of inclusions in meta-peridotitic SDDs also indicate a subduction-related origin (e.g., Na-rich clinopyroxene inclusions and anomalously light δ 13 C values, [6]). This may suggest a higher degree of mixing of fluids derived from subducted oceanic crustal and mantle sources prior to diamond precipitation in meta-peridotitic SDDs compared to meta-basaltic SDDs. This is evidenced from highly variable core-to-rim δ 13 C trends in meta-basaltic SDDs (e.g., δ 13 C core-to-rim = − 20 ‰ to − 5%, [151]) attributed to mixing of carbonated melts derived from crustal and primitive mantle sources [6,378]. SDDs characterized by Fe alloys and sulfide inclusions also show light δ 13 C values (e.g., the CLIPPIR diamonds, δ 13 C = − 26.9 to − 3.8 ‰ and the Collier-4 diamonds, δ 13 C = − 26.0 to − 8.0 ‰, see Sect. 4.3) and Smith et al. [55] suggested that the extremely heavy δ 56 Fe (0.79 to 0.90 ‰) compositions of metallic inclusions in CLIPPIR diamonds represent Fe-Ni alloys that crystallized during the serpentinization of peridotite in oceanic crust. Associated age dating of a CLIPPIR diamond [53][54][55] would place the minimum age of deep, modernstyle subduction in the Mesoproterozoic. As is the case with the geochronological database of SDDs, more isotopic data are needed to constrain the source of C-bearing fluids and melts in the deep mantle.

Coda
The study of diamond, natural and synthetic, has seen considerable growth over the last 20 years. This is coincident with major developments in analytical methods and improvements to associated instrumental technologies that have allowed measurement (and in some cases, imaging) of impurities (e.g., defects) in diamonds at extremely low concentrations or of inclusions that are increasingly small and in the past, not identifiable. Moreover, recent technological advances have allowed extraction of data from inclusions and/or diamond that was previously overlooked. For example, it was not until the early 2000s that the first systematic X-ray crystallographic studies (e.g., [210].) of mineral inclusions in diamonds were published where important data regarding variations in unit-cell parameters (as a function of entrapment pressure) and relations between the crystallographic orientation of inclusions and their diamond hosts were rigorously treated. As a consequence of such works, several subdisciplines of diamond research have emerged, such as elastic geobarometry (e.g., [214,220,246]) and crystallographic orientation relations (CORs) (e.g., [216,237,[453][454][455]) and have improved our understanding of the P/T conditions of diamond formation and the protogenetic (or syngenetic) nature of mineral inclusions in diamond (see [219] and references therein).
In general, the goal of geologic diamond research is to understand in what geologic settings, under what thermodynamic conditions, and by what chemical reactions do different types of natural diamonds form. As the analysis of diamond and its inclusions is the only means by which to directly sample the deep Earth, it is often used to support models or hypotheses regarding large-scale Earth processes (e.g., geodynamics of mantle C and the evolution of tectonic processes, see Sect. 5 and references therein) or general planetary processes (e.g., planetary differentiation, compositional evolution of the mantle, crust and atmosphere and sources of volatiles required for life, C (e.g., CO 2 , CO 3 ), O (e.g., O 2 , O 3 ), N (e.g., N 2 , NO 2 ), and H (e.g., H 2 O) (e.g., [456][457][458][459]). Fortunately, time and continued exploration has afforded diamond geologists with increasingly statistically robust datasets that, for lithospheric diamonds, contain thousands of different mineral and fluid inclusions (e.g., [42,52,134]). Careful examination of such data has (and will continue to) improve our understanding of how and where diamonds form in the Earth's Mantle.
Lithospheric diamonds precipitate from supercritical fluids and/or supersolidus melts with varying concentrations of C, O, and H and dissolved solutes such as silicates. The speciation of C in solution (e.g., CH 4 or CO 2 ) and the chemical reaction by which C-species are reduced or oxidized to form diamond, is controlled by the redox conditions (i.e., f O2 ) of the fluids and diamond substrate into which such fluids may percolate. Lithospheric, peridotitic diamond is typically associated with melt-depleted substrates that comprise the cratonic mantle keel where the majority of lithospheric peridotitic diamonds are assumed to reside. The formation of eclogitic diamonds is likely more complex; it involves infiltration of carbonated melts and/or fluids derived from subducted oceanic lithosphere into the surrounding, relatively reducing, mantle lithologies or within the subducting slab. However, eclogitic diamonds are overrepresented with respect to the predicted abundance of eclogite in the lithospheric mantle and thus must form from processes that are relatively more efficient (condusive to higher growth rates) than those responsible for peridotitic diamond. Stachel et al. [134] suggest that diamond is stable in eclogite at higher f O2 than in peridotite and that precipitation of diamond from reduction of CO 2 -bearing fluids or isochemical precipitation in a setting with sharp redox variations and large volumes of fluids supplied by dehydration of the subducting slab, could result in nucleation and growth of eclogitic diamond that is relatively more efficient than peridotitic diamond.
The dataset for sub-lithospheric diamonds is relatively small, and thus, models for the formation, growth, and transport of SDDs to the surface are still strongly debated. However, it is likely that SDDs also form from similar C-O-H fluids and melts, although the compositional range and redox properties of such mediums are not completely known [6]. SDDs are broadly grouped into meta-peridotitic and metabasaltic paragenesis where the former shows heavier C isotopic compositions, similar to mantle C, and the latter shows relatively lighter C isotopic compositions more akin to subducted oceanic crust. It follows that meta-peridotitic SDDs may source C-bearing fluids from the mantle segment of the subducting slab and meta-basaltic SDDs may source fluids via melting and dehydration of the hydrous and carbonated oceanic crust segment of the subducting slab [129]. The study of inclusions in SDDs has provided strong evidence for deep subduction and stagnation of lithospheric material in the transition zone and shallow lower mantle and thus has major implications for the extent of Earths deep carbon and H 2 O cycles (e.g., [61,92,274,276,302,383]). Inclusions in SDDs are often composite in nature and show evidence of complex unmixing (phase retrogressions) histories that indicate transport from lower mantle to upper mantle conditions. This may be associated with mantle-plume upwelling and transport via melts during redox-freezing-melting cycles, but more work is required to constrain these processes.
In general, most of the work on natural diamond focuses on the mineral and fluid inclusions they contain, but it is likely that additional methods to interpret data related to impurities (e.g., substitutional and interstitial defects, aggregation states, growth patterns, and structural dislocations) need be developed if the more complex questions regarding the formation of diamond in Mantle are to be addressed. Thus far, impurities (as defined in Chapter 3) have been used to determine the residence time and temperature of diamonds from both a qualitative (e.g., dislocation networks indicative of elasto-plastic deformation attributed to long, high-P residence times) and quantitative (e.g., calculation of mantle residence time/temperature based on N-aggregation state or the degree of platelet degradation) perspective. However, they have not been related, in any rigorous way, to the conditions of diamond formation in the mantle, a potential future direction for the geological research of diamond.